Actually most plastics can be used in the microwave with some exceptions. I learned the hard way that microwaving anything containing primarily tomatoes with some oil does cause stains in a Rubbermaid storage container.
Some people are concerned about toxins leaching out of the plastic into the food. I have read that we cannot get enough toxins in the small amount of plastics and time we use plastic to endanger our health. I do limit the times that I microwave in plastic storage containers.
Melamine is a different kind of plastic. It has different ingredients and it's surface is much more smooth and without pores. It's surface is slick and solid unlike storage containers.
We had Melamine dishes when I was a child 55 years ago. Once we had a microwave we used Melamine in the microwave only to heat food. Some research suggests that when it's heated to an extremely hot temperature it will bubble and release a toxic chemical. I believe it to be totally safe when use to only heat foods for a short period of time. I wouldn't cook foods in melamine.
Later: I did find that some Melamine type dishes do say microwaveable and one site I looked at said to use only Melamine that says it's microwaveable. I agree with MartyMOMMA's description of what happens to Melamine when it's used for cooking rather than just heating.