Pikmin are something of a cross between plants and animals, whereas pikpik carrots are the same as normal carrots (except they come in red, blue, yellow, and gold).
Pikmin are plantlike, and seem to be closest to carrots. Captain Olimar takes note of this and names them Pikmin, after his favorite food of pikpik carrots.
Olimar named the Pikmin such because of their similarity to the red, blue, and yellow pikpik carrots in his favorite soup.
Mushroom Pikmin are Pikmin that have been transformed by the spores of a creature called a Puffstool. Affected Pikmin turn purple and try to attack Olimar and normal Pikmin. This effect wears off after a while.
The original Pikmin involves you hunting for 30 pieces of your ship within a limit of 30 days, with each day being 11 minutes real time. Thus, you have a time limit which makes the game more stressful than usual. If you like a challenge by getting items before time is up, then this game is for you. However, because you only have 30 days, the game will not last that long. Pikmin 2, however, involves you searching for treasure (and even dead bodies of creatures you defeat) in order to pay back the 10,000 Pokos that led the company of Hocotate Freight into debt. Once your debt is paid, you can gather the remaining treasures, and after that you can still raise Pikmin. You have unlimited days to complete all of the tasks, which means some days can be spent just getting more Pikmin while others may involve completing two caves. Not only is there a challenge mode, but there is also a two-player mode to go along with the adventure mode. Most people select Pikmin 2 as the clearly better game, simply because it adds a two-player mode, a challenge mode, and a very intense and thorough story mode that you can accomplish at your own leisure.