Generally speaking, 1990s and 1990's mean the same thing. 1990s uses a more modern style of punctuation (or rather, a lack of). 1990's is a more formal or traditional use of the apostrophe. I believe what @smatterer says about the use of the apostrophe as a contraction or to show possessiveness is also correct, but both of those usages are fairly rare.
To answer your question: 1990's and 1990s both refer to the decade, years 1990 through 1999. 1990's can also refer to the two rare usages mentioned above. So if someone tries to tell you 1990's can't refer to the decade, they're technically wrong. Keep in mind that a style guide will prescribe a specific way to write, but the style guide is not suggesting that it's correct and other style guides are incorrect. Don't confuse the rules of a style guide with some website or person trying to tell you what's right or wrong.
A similar question is asked and answered in greater detail here:
Do decades ever get apostrophes?
If you're not familiar with style guides, check out The Chicago Manual of Style, one of the most famous American style guides. It can save you a lot of time and headache if you're writing something big (or even small):