DDR- Double Data Rate. Not backwards compatible with normal PC133, PC100 or PC66 RAM.
PC***- the asterisks refer to the speed of the RAM. PC133 would work in a PC100 system, but at the lower speed.
DDR266, DDR333, and DDR400 are the main varieties of DDR RAM out today. DDR400 would work in a DDR333 or 266 (or other) system but at the lower speed.
If you place a stick of RAM with a lower speed into a computer that can accept the high speeds, you limit the bus to that speed RAM. So it is OK to go above the speed RAM your computer can take but not below.
SO-DIMM- Small Outline RAM. Can be DDR or not, just means it is smaller.
SIMM- Single Integrated Memory Module. Used years ago, now everything is a DIMM. I am just telling you about SIMMs so that you know what they are.
DIMM- Double Integrated Memory Module. Used today.
Your friend's Mac will use DIMMs, but I do not know about DDR... most likely not.
Every Mac.com has information on what RAM speeds the computer will take.