The similarities between the Mayans and the ancient Egyptians are slight and can easily be put down to coincidence.
The similarities between the pyramids of the two cultures is NOT a coincidence!
If you have limited engineering and technical capabilities (e.g,no iron Ibeams) but you want to make a heck of an impressive construction the way you do it is to build a mountain. You make a big base and pile something a bit smaller one level up. I can't think of anything else that you would do. This produces a step pyramid. It is the combination of technology and physics not coincidence that produces the similarities.
In fact, the other, more famous pyramids of Egypt are step pyramids too. The steps are smaller (a couple of meters in the most outside layers) but they are still steps. Then there was (only a little left) a capping layer fitted over the steps to make it smooth. This is a heck of a lot of work though and the Mayans wanted to get on top of their pyramids so they were less inclined to do this.