basic doubts
1) Impedence matching: for best signal transfer (lowest loss, no reflection) you want to match the output resistance of one system to the input resistance of the next system. For example looking at TV antenna system, you want to use an antenna with impedance of 70Ohm, 70Ohmcable and a receiver with input impedance of 70Ohm.
2) They may actually be exactly the same. BUT, to remove digital noise from analog circuits, the two ground places are separated. They may be connected at the power regulator, but the analog circuit may even have it's own power supply keeping the two ground planes completely disconnected. The main idea is to protect the analog circuit from seeing the high frequency switching noise from the digital circuits.