MacBook Pro Display Adapter

Yes, as long as your new MacBook Pro is of the 13" variety, then you will have no problems.

While Power Adapters technically have different model numbers (to associate them during repairs), the wattage is what you need to look at when considering to use on on a machine. 15"/17" MacBook Pro's require 85W Power Adapters, where as, the 13" MacBook Pro and MacBook use 60W Power Adapters.

Hope that clears it up for you.

The MacBook Pro has the same number of pixels as the Cinema Display but a smaller area to show them on. That makes the pixels on the MacBook Pro smaller. Since windows and text are a certain number of pixels in size, screens with smaller pixels will make them appear smaller.

The solution is to choose a lower resolution on the screen with smaller pixels (the MBP in your case). Choosing a lower resolution means that each pixel of data will be drawn across multiple physical pixels, making everything bigger.

I can't tell you exactly what resolution to use on your MBP to get things close to the same size, but it shouldn't be hard to find out with a little testing.

Open System Preferences -> Displays and go to the Display tab of the window on your MBP.
Check the Scaled radio button and pick the second resolution on the list that appears. If that isn't big enough, move on to the next (lower) resolution, etc. Stop when you get to one that makes things similar in size across both displays.

Note that, as a result of this, your MBP's display may not look as nice. Things won't look as crisp and some resolutions will have to stretch things sideways.