Not necessarily, and no.
Resolutions and settings are configured for each seperate screen, so you can have them how you please.
There are two ways of doing a dual video setup.
1) Get a video card that is capable of outputting to two displays by itself (Geforce 4 Ti range can do it, older Matrox cards can)
If you've got the money / the card already, this is the better way to go in my opinion. The card can be configured (in your Display settings) to output to two different sources at once, whether they be two screens, screen + TV, or whatever (depending on the card).
2) Get two video cards
By having either 1 AGP + 1 PCI card, or 2 PCI cards, You can simply hook up a screen to each one. A lot of people simply buy a cheap, 2D PCI card for this so it can display stuff while they use the other card for games / work / etc. This is a little more complex to set up, as settings may need to be tweaked a little to get it working properly, plus the cards may not like each other. :)