No, switches are not just simplified routers. Although many devices combine functions of both routing and switching, the two functions are distinct. Switches create networks, routers connect distinct networks together. Switches operate using only MAC-addresses, while routers also use IP addresses. Switches have many ports in the same subnet, while routers can only have one port per subnet. Devices that combine these functions still maintain a distinction between routing and switching, as they will separate 'switched' ports from 'routed' ports due to the requirements of the different functions and hardware.
To show some of the nuances: professional grade routers will perform internal switching functions (such as CEF), and some 'layer 3' switches Route (if they are layer-3 switches), but the operations are distinct.
It is useful for anyone interested in networking to become familiar with the OSI Model, which describes how computers and other devices talk to each other. The OSI Model breaks communication into seven layers, including the Application layer, which is the program you, the human, are working with, the Network layer or Layer-3, which deals with IP addresses and Routing, and the Data Link layer, or Layer-2, which deals with physical hardware addresses. Also, when you hear terms like TCP, ports, sockets, sessions, etc., these are also represented by the OSI model, so it's useful to learn.
Routers operate with IP addresses at the OSI Layer-3 or Network Layer and Switches operate with MAC addresses at the OSI Layer 2 or Data Link Layer.
Some devices, such as consumer wifi-routers, combine both a switch and a router in the same device (for instance a wifi router with 5 extra ports on the back). Other devices, such as cable or DSL modems, still function as a router because they route packets between your local network, and the remote network, and perform layer-3 functions such as NAT.
The operations of Routing and Switching are distinct however, and operate on different layers of encapsulation, different OSI layers, and with different addresses, as described below:
In detail:
Switching
We will start with a Layer-2 Switch. This is your standard switch, that includes all un-managed switches, and even managed switches that only operate at the Data-Link layer. This switch receives frames and compares them to a MAC-Address-Table (which is distinct from the ARP table in that it has MAC Addresses and Ports, rather than MACs and IPs). It uses this information to forward frames either to one, many, or all ports depending on whether it is a unicast, multicast, or broadcast frame. If it is a unicast frame, but it does not know which port to send it to, it floods it to ALL ports, except the port the switch received the frame on. Of course there is more detail with CAM tables and VLANS, but in short: Switching moves frames based on hardware addresses, switching can only move frames within the same subnet.
Routing
A router routes between subnets. In fact, on a router, you cannot put multiple routed interfaces on the same subnet - because a routers function is to move packets between layer-3 subnets. The router thus receives frames, containing packets off a port. If frame's destination (mac-address) matches the router (either as unicast or broadcast), the router will then look at the IP-packet contained inside the frame, and make a routing decision based on the IP and subnets. Once the routing decision is made, a switching decision is made to determine which port and layer-2 destination to send the packet to, so it can be re-encapsulated at Layer-2. For more information about the switching conducted by the router, see Cisco Express Forwarding, for example.
How the computer gets through the gateway:
So how does the computer reach its gateway? The computer itself has a route to its gateway. It knows that "if an IP is not on my subnet, I need to send the packet to this gateway address to get out," Thus, since all devices process top-down through the OSI-model, the computer will do an internal routing lookup first (layer-3) to decide wither a device is within its subnet. If not, it will arp (layer-2) to find the mac-address of the default gateway, and will encapsulate the IP packet for the remote host within a frame addressed to the router. The frame will be switched across the network using layer-2 headers and MAC addresses, within the same subnet, until it reaches the router, where its layer-3 IP addresses are looked at, and the decapsulated packet is routed between subnets.
Layer-3 Switches
The other scenario I haven't covered is the Layer 3 switch. These switches operate the same way as described above. They are switches, but they can have specific ports, physical or virtual, designated as routed ports. These routed ports operate as gateways between subnets, (often VLANs within a switch) while the switched ports continue to only operate at Layer-2.
Part of the distinction between layer-2 and layer-3 devices is reflected in the hardware and memory of the devices. As Cisco explains, layer-2 only devices have a CAM (content addressable memory) table containing the MAC-Address-table. Layer-3 devices additionaly have a TCAM table, which handles mapping between routing, layer-2 and layer-3 addresses. Because of the physical hardware differences, you will see price differences in hardware that is a pure layer-2 switch, a layer-3 switch, and a router.
Best Answer
If you only temporarily need to speak to 192.168.10.10, this will be the easiest thing to do.
I'm simplifying the following a bit to explain better:
For your computer to talk to any computer, your system must have an entry in its local routing table (or Forwarding Information Base) for that subnet.
A subnet is a network address plus a subnet mask. (Note that the subnet mask can be in dotted form (255.255.255.0) or CIDR form (/24) - they express the same thing though certain things want only one or the other).
The subnet mask says how many bits long the network address is. All the bits that are 0 in the subnet mask (the last 8 for 255.255.255.0 or /24 - which is the last number in the dotted-four notation) will be 0 for the network address. A full IP address actually given to a machine will not have 0's in that spot - but routing table entries work with network addresses.
A routing table entry consists of a subnet plus an interface, and tells your system that if your system sends traffic out of that interface, it can reach that subnet.
You get a free routing table entry whenever your system gets an IP address plus a subnet mask, either by you doing that manually or it happening automatically via DHCP.
If you have a single ethernet adapter, and it gets the IP/subnet mask 192.168.7.4/24 via DHCP, the /24 is saying that your system can send something out of that ethernet adapter and reach anything else beginning with 192.168.7.
If you are in a typical LAN situation, where other machines on that LAN have the same network address (192.168.7) and subnet mask (/24 or 255.255.255.0), this works.
You also get a free routing table entry for your loopback address. 127.0.0.1/8.
If you add another ethernet interface, let's say a USB one, and manually configure it with an IP, say 192.168.10.1, the same thing happens above with free routes. Assumne you assigned the USB ethernet adapter 192.168.10.1 with subnet mask /24 (or 255.255.255.0). So now your computer can get to 192.168.10.7 because it has a route to it.
What if:
you have two adapters that can reach the same subnet?
If they differ in subnet mask, the more specific one (the higher CIDR number) will "win" and will be used. (One interesting side thing to mention is that you can think of /32 - or subnet mask 255.255.255.255 - as a shortcut that means "this specific IP" - so you can make traffic originating from your local system destined for a specific IP to go out a different interface - like a VPN interface - if you wanted by making a route table entry with a /32.)
Otherwise, there's another value called the metric - the adapter with the lowest metric will be used. Typically you'd set faster adapters to have lower metrics. Your wired adapter should have a lower metric than your wireless for this reason.
If they are same CIDR and equal metric your system might pick one and then stick with it, or load balance between them. This may be configurable depending on your OS and drivers.
your system wants to send traffic somewhere but it doesn't have a routing table entry? It uses the default gateway - this consists of an IP address (which must be reachable by some other local routing rule.) Typically this will point to your Internet-facing router on your same LAN in a home setup, and is set by DHCP though you can set it manually too as you probably already know.
you don't have a default gateway? It drops the traffic and doesn't send it.
you have multiple default gateways? It will probably either pick a random one and stick with it or it might load balance between them. This may be configurable depending on your OS and drivers.