Methacrylate does seem more technical. I'm a native speaker of English with a semi-decent vocabulary, and I had to look up what it meant.

Acrylic is a word everyone knows, but on its own, it's not specific enough--it can refer to acrylic paints or acrylic fibers, for example. And I'm not sure if everyone knows that these materials can be referred to as acrylic sheets or acrylic glass.

I think Plexiglas is the most common term in the US, with the genericized plexiglass as a less common variant spelling. Alternatively, it's sometimes referred to by the trademark Lucite. In the UK, the trademark Perspex is instead more common.


EDIT: With ChrisH's help, I've come up with a pair of hopefully less misleading charts from Google Ngram Viewer, included here because everyone loves charts. First, when set to "American English", Google gives us this chart, supporting Plexiglas as the most popular:

AmE

And another chart, with Google Ngram Viewer set to "British English", which suggests that Perspex is more popular over there:

BrE


These are acrylic sheets made of acrylic plastic, or, as sometimes called, acrylic glass (Polymethyl methacrylate).


Colloquially the trademark Perspex (also Lucite) is used generically for clear/translucent acrylic sheet -and even for similar looking materials.

Edit I think perspex is more common in the UK, while lucite (or plexiglass as in another answer) more common in the US, and ngrmas would appear to agree.