Craft foam is
EVA foam. Both are a closed-cell foam that is relatively durable, stiff yet flexible, and easily heatformed. Craft foam just happens to be thinner and comes in different colors, but it's all roughly the same thing.
Craft foam has the advantage of being readily available at arts&crafts stores, coming in a variety of colors. The downside is that they tend to be thin sheets, usually 2mm, 3mm, or 6mm, in either a 9x12" size or a 12x18" size. The thickest foam also comes in only black or white in the smaller 9x12 size.
Now, as far as other thicknesses, you can definitely use the anti-fatigue floor mats. You can find them at hardware stores like Lowes, Home Depot, or Harbor Freight, or even big box stores liek Walmart, usually in the garage/automotive section. They can come in bigger sizes (2ftx2ft tiles, for example) and they may or may not have some kind of texture on one/both sides. The downside is that these floor mats usually only come in their standard grey/black color, and only in a few thicknesses (0.75-1"), so they'll require a bit more work to make them another color (For example, using blue craft foam for blue armor may greatly save on paint, whereas with the anti fatigue mats, you'd need to completely coat it to change the color)
An option would be to custom order it online. I was pointed to a foam store in San Francisco that does orders on 40x80 sheets of closed cell EVA foam in a variety of thicknesses. I'm planning on getting a sheet of .25" foam to make some armor for a movie-style MMPR Green Ranger. I live locally so I can actually go their warehouse and pick it up in person.