Oh, I see. "Hand-woven" is the more generic term. There are various ways to produce rugs by hand, and they look very different (quite independent of design).
Piled rugs (like the one your mom bought) are hand-woven (i.e. made entirely by hand) AND hand-knotted. There are different types of knots used in different areas, but they all result in a pile, this soft velvety surface. (You should google "symmetric knot" and "asymmetric knot", then you get pictures.
Kilims can also be hand-woven or machine-made, but they are flat-weaves, that is you get a flat, even, less shiny appearance. You should look up kilims on ebay, then you see. With kilims, usually the back looks exactly like the front, and you can use them either way round. There are very beautiful hand-woven old Turkish and Navajo Kilims.
There are also Sumak rugs, also hand-woven, which are some kind of hand-embroidery, also flat-weaves, but the underside looks messy. Lots were produced in the Caucasus a century or so ago.
And there are needle-point rugs (usually European), made similar to needlepoint cushions, these can also be hand-woven (stich by stich) or machine made.
These are the most common ones, there are some more that one rarely finds.