These days we use gesso as a generic term used for the initial coat applied onto a support (or surface) before you paint on it. Maybe because it sounds less DIY than primer. The purpose of gesso is to protect the support from the paint, some of which contain components that could damage it, provides the key (surface) for the paint to stick to, and affects the absorbency of the support. Gesso dries to a matt, gritty surface that provides adhesion for the paint. To get a smoother finish, you can sand it.
Most ready-made canvases are primed with an acrylic gesso, and are suitable for both oils and acrylics. You can also get canvas primed with traditional gesso for oil paint only. The packaging on the canvas will tell you what type of primer was used.
If you're unsure whether a canvas is primed or not, compare the front and the back. Sometimes the color will make it immediately evident, otherwise look at whether the grain of the fabric has been filled in or not. If in doubt, give it another coat.
The difference between student and artist grade acrylic gesso is in the quantity of white pigment in it. The more pigment, the more opaque it is and the more likely that one coat will provide a consistent cover. The gesso filler and pigment may also be ground more finely, giving a smoother finish when dry.
Traditionally canvas was sealed with rabbit-skin glue. If you've ever been into a studio where some of this is heating on a stove, you'll know why less smelly acrylic alternatives are popular!
