the old power supply is probably 60 watts and the newer computer is 85 watts.
it will work, but your computer will not charge as quickly. or may even slowly discharge if you're using the computer while you're plugged into the older power supply.
http://support.apple.com/kb/HT2346
While the link is good read; however, you made some serious assumptions that I need to correct.
OP, yes it is safe. Since you had a white macbook, it came with a 60watt power supply. If you bought a 13" Macbook Pro, it too would come with a 60watt and thus would charge at the same rate no matter which power supply you use. However, if your macbook pro is a 15" (or a discontinued 17"), then it would have come with an 85watt power supply which will slow the charging or not charge it at all (it should run fine, but to fully charge you will need to not use it when hooked to the 60watt power supply).
The Macbook Air's come with a 45watt power supply so they too would be unaffected since you can always use a larger power supply (just means the power supply won't be used to its "full" potentional).