There is no issue with using the same SSID and PWD for the 2 channels. If you use it this way you can take advantage of the 5ghz when you're local to the AP, but fall back to the 2.4Ghz when interference it too much.
However, in some cases, if your SSIDs are the same - you will have a wireless connectivity problem when you are connecting client that was 2.4Ghz adapter ONLY. (adapter gets confused).
Referring to the above I would recommend to use different SSIDs for the 2 channels (troubleshooting purposes too).
Supported capability on your clients
iw phy on GNU/Linux should list what you want (and a lot more) about your wireless interfaces, although it's a bit confusing at first sight.
What you're looking for is if your network card works in dual-band mode. You'll then see Band 1: and Band 2: section, first one usually for 2.4Ghz and second one for 5Ghz. Under each bands you'll see Bitrates (non-HT):, listing the supported bitrates for 802.11bg in 2.4Ghz or 802.11a in 5Ghz.
You're also looking for HT20/HT40 under Capabilities: for each band. It means 802.11n is supported. HT20 is for 20Mhz width channels, HT40 for 40Mhz width.
If you want to know more about 802.11n capabilities, for example number of spatial streams (for MIMO) and supported rates, look at the HT TX/RX MCS rate indexes supported: line. 0-15 means MCS Indexes from 0 to 15 are supported, ie. it can works in MIMO 2x2 with data rate up to 130 Mb/s in HT20 or 270 Mb/s in HT40. Additionally, if RX HT20 SGI and/or RX HT40 SGI is listed under Capabilities:, it means Short GI (400 ns) is supported so max data rate is 144 Mb/s for HT20 and 300 Mb/s for HT40. See here for a list of MCS Indexes: https://wireless.wiki.kernel.org/en/developers/documentation/ieee80211/802.11n
Frequencies: list supported frequencies and associated channels. Some may be disabled because either your hardware or software doesn't support it, or because your regulatory domain doesn't allow it. If your WiFi access point broadcast signal on a disabled channel you will not be able to connect. You can see which channels are allowed in your area here: https://en.wikipedia.org/wiki/List_of_WLAN_channels
Additionally you may see VHT Capabilities and other VHT related info. It's about 802.11ac, but your access point does not support it (neither the chipset you indicated), so you can ignore it.
Access point configuration
I would really recommend you to keep your WiFi access point configured to broadcast on both 2.4Ghz and 5Ghz. Nowadays, 2.4Ghz is very crowded and is more subject to interferences, when 5Ghz has much less devices using it. Problem is that 5 Ghz is generally supported only on recent or high-end devices whereas 2.4 Ghz is the default band used on WiFi devices. Also 5Ghz signal range is less than 2.4Ghz and more subject to degradation due to obstacles.
Using both bands enables you to have wireless on the most devices (either because they don't support 5Ghz or because the signal is degraded, so they fall back on 2.4Ghz) while having better performances in high-end/recent devices (because they're using the 5Ghz band).
Finally you shouldn't worry about B, G and N on your access point, you should select the mode which provides the three standads (mixed) so that older 802.11g (802.11b devices are very rare nowadays) devices can still connect and newer 802.11n work at full speed. Also only 802.11a and 802.11n work in the 5Ghz band. (there's 802.11ac too but you're not working with it)
Maybe you'll also see a channel setting. Usually leaving it to the default will do the job, your access point should be clever enough to select the best. (and it prevents you from selecting a channel overlapping on others creating even more interferencies)
Link between the two
iw dev on GNU/Linux will show you how your client and your access point are connected. Ideally it will be in a channel on the 5Ghz band (and allowed in your area) with 40Mhz width.
Best Answer
If you have high quality Wi-Fi client devices, it's best to use the same SSID for both bands so your clients will automatically roam to the band that suits their needs best.
If you have low-quality Wi-Fi client devices, you might need to second-guess their band-choice decisions, so you might want to have separate SSIDs.
Your MacBook Pro should not have shown you two networks with the exact same name, unless you had accidentally configured two different security types for the two networks. Or maybe you thought you had configured the exact same name for both bands, but you'd accidentally put a space at the end of one of the names and didn't notice.
Your iPhone 4 doesn't have a 5GHz radio, which is why it can't see your 5GHz network. I suspect the same is true of your HTC Desire HD.
I recommend that you leave your 2.4GHz network set to 20MHz-only. Using 40MHz in 2.4GHz doesn't leave enough room for other uses of the band, such as Bluetooth. All of Apple's N-capable gear limits itself to 20MHz operation in 2.4GHz (even if the third-party Wi-Fi AP is configured to allow 40MHz operation in 2.4GHz), in order to leave room for Bluetooth. So your MacBook Pro is only going to use 40MHz-wide channels in 5GHz.