Calling someone a "Darwinist" or "evolutionist" is about as ridiculous as calling someone who accepts the fact of gravity a "gravitationalist," or someone who believes the earth is spherical a "sphericist."
Darwinism is wrongly thought by many fundamentalists to be the "religion" of atheists. It's true that most atheists accept Darwin's theory, but that fact is irrelevant to their nonbelief in a deity. They simply see no reason to reject something that's obviously true (i.e., it doesn't contradict some other belief that they refuse to give up).
Such a tactic is dishonest. The theory of evolution is not an ideology. Ideologies are PROSCRIPTIVE--they make value judgments and say what should and shouldn't be done. The theory of evolution, like all other scientific theories like gravity, relativity, etc., is DESCRIPTIVE--it describes and explains facts. Such theories are testable by analyzing them to see what the predictions that they make, and then seeing if those predictions match the facts.
For example, applying the theory of relativity predicts where the stars will be. We look at our hubble telescope and see that lo and behold, the stars are indeed where the theory predicts them to be!
The theory of evolution predicts that the evidence will show that humans and chimpanzees are closely related. We look at human chromosome 2, and see that it's virtually totally analagous to two chimp chromosomes, and lo and behold, human chromosome 2 has a fusion site with telomeres in the middle of the chromosome! (Imagine taking the 2 chimp chromosomes and "scotch-taping" them together--that's what human chromosome 2 looks like).
Often used to refer to things far outside the purview of Darwin's theory of evolution, which relied solely on natural selection as the mechanism for change.
Darwinism is also a term used for religious atheist adherents of the theory who constantly talk about evolution, won't accept any criticism about their wrong atheistic naturalistic interpretation of evolution and their model for evolution and those who religiously worship Darwin. An atheist who does these things can be called a "Darwinist".
Darwinism is closely related to naturalism.