Texture is a clue. Acrylic tends to build up fast because of its quick drying properties, giving it an impasto texture without trying. Of course, there are various media that can be added to thin or retard drying, etc. There is a difference in sheen, as well, but I don't know how I would describe it. Best thing you can do is compare one of both kinds side by side. One final test, if it's your own property, is to find a bit of raised paint in an innocuous area, and press down with your fingernail. If it leaves a little indent, it's probably acrylic, which is a plastic of course. If it doesn't yield, it's probably oil.