Before I start, tho', let me qualify all this by saying I am neither a scientist nor theologian.  Just a guy who took some philosophy classes once upon a time. :) 

The elder of the two is obviously creationism.  The standard Christian version^* dates back well before the birth of Christianity itself, coming from the Hebrew Old Testament.  It is therefore a part of our culture, even if you're not a particularly religious person.  Adam, Eve, and Eden are all pretty well known concepts. 

But what exactly is creationism?  Basically, it's mythology.  It tells the story of an omnipotent supreme being who creates the world and all its inhabitants in seven days.  What it most definitely not, however, is science.  Nor is it a theory.  A scientific theory is something that has been tested in various ways to determine its validity and that can, most importantly, be duplicated by others.  Take Newton's old theory of gravity.  He came up with the concept and tested it.  When he shared his results with his fellow scientists, they tried to recreate those findings.  Guess what?  They did.  That's how something becomes a valid scientific theory: observations, tests, and more tests. 

More importantly, scientific theories do not set out to prove a particular point of view to the exclusion of all else.  That's what creationism does.  It starts out with the premise that God created the world, and then tries to find (some would say manufacture) facts to support that proposition.  Real science, on the other hand, takes the facts first, puts them together, and draws conclusions.  If the body of scientific fact does not support a theory, it is discarded. 

And that is where the theory of evolution comes from.  It all started back with Darwin's observations in the Galapagos islands and other places.  He examined the facts and developed his theory around them.  He and his successors did not have some kind of ulterior motive, as some of the creationism supporters seem to suggest. 

Creationism supporters like to point out that there are holes in evolutionary theory.  Those omissions, they claim, make the entire theory worthless.  I find that hard to swallow from a group whose best evidence comes from a text written thousands of years ago in a language most of them can't speak, much less read.  I would hope they would not use that same logic in their religious studies, or they would likely find themselves disappointed with their chosen faith.  All theories, be they political, scientific, or religious have holes or other problems.  If they didn't, they wouldn't be theories, now would they? 

Creationism and evolutionary theory are two different animals.  There is no reason, however, that they cannot be reconciled.  It's just as possible that some sort of supreme being set up the planet with an evolutionary scheme, and then walked away and let things run their course.  There's no reason one side must be right at the expense of the other.  Since they are different in nature, it's quite possible for them to live in harmony.

Many on the Christian right want creationism to be taught in science class along with evolution.  That's just plain silly.  When we teach about birth and human development we don't include the story of Athena sprouting from Zeus's head, do we?  Of course not.  The theory of evolution is exactly that, scientific theory, and should be taught as such, just like theoretical topics in the other sciences, philosophy, and law.  Creationism, on the other hand is part of a religious belief system. 

Before I go further, let me say this.  I do think that in some places evolutionary theory as the way humans came to be is taught as gospel.  Ooh, poor choice of words, huh?  And that, I think, is wrong.  Just as it is wrong to teach that market capitalism is the only economic theory that is viable in the world.  Theories should be evaluated and have conclusions drawn about them by the students, not the teacher. 

If creationism has a place in schools, it should be in a broad class about world religions.  Heck, you could surely teach a semester on just the various creation myths from around the world.  That would put creationism in its social, historical, and religious context and allow for a better understanding of exactly what it is than just cramming it down kids throats. 

Bottom line, religious dogma of any kind has no place in the public schools.  Except as part of an education, not an indoctrination.  If you are really so concerned that your child learns the truth as YOU see it, than teach that truth at home.  Don't foist it on the rest of us.