Yes, it's the comma splice.
What's the difference between a regular old comma and a comma splice? Why, I'm glad you asked. Amongst doing other noble things, a comma indicates a brief pause in a passage or separates points in a list. A comma splice, however, is evil and confuses things, transforming grammatically sound sentences into unrecognizable strings of confusion.
The simplest way to explain the difference between a comma splice and a regular comma is to show you, so let's play a game.
Which of the following passages is correct:
A) Dinglebert smells of cabbage and Lucy thinks it's gross.
B) Dinglebert smells of cabbage, and Lucy thinks it's gross.
How about these ones:
1) My eyes are green and my teeth are green too.
2) My eyes are green, and my teeth are green too.
There are twenty-four pages dedicated to the various uses of the comma in The Chicago Manual of Style (16th edition). Yes, you read that correctly; I said twenty-four pages. When we get to the part about comma usage in relation to independent clauses joined by conjunctions (I used "and" in all of the above examples), here's what it says:
"When independent clauses are joined by and, but, or, so, yet, or any other conjunction, a comma usually precedes the conjunction. If the clauses are very short and closely connected, the comma may be omitted unless the clauses are part of a series."
Above, Dinglebert's answer A is incorrect, because it contains two independent clauses joined by a comma without the conjunction. That is a comma splice. Naughty, naughty. Dinglebert B contains both a comma and a conjunction, and the two clauses are not closely connected. Dinglebert B is punctuated correctly.
The true to life sentences about my eyes and teeth being of the same colour are a different story altogether. In the first example, our independent clauses are joined by the conjunction "and" without a comma. The clauses are of close relation, the subject is the same (me), and they are short. Should there be a comma in between?
There are some exceptions to this rule (of course!), but here's a simple way to tell if you'll be needing a comma in a situation like this: If there is the mention of a new subject in the second independent clause, there should be a comma before the conjunction. If the subject is the same (or is omitted so it's assumed it is the same) and the clauses are short, you can leave the comma out.
What's your guess for the second example?
So, don't automatically assume that every time you use a conjunction to join a pair of independent clauses you need a comma. First, consider the relation of the clauses. Next, consider their length. Then consider if they might be better as separate sentences (a period rather than a comma may solve the problem). If, after all that, you decide to keep the clauses together, please use the appropriate protection. The offspring of poorly punctuated independent clauses can be long, unwieldily, and just plain unpleasant to look at.