what is the word for the inside frame in a painting?

STRETCHER BARS

I think that you might be asking about the wooden frame that the canvas is stretched over. When the painting is finished it fits inside the edges of the outside frame.

They are called canvas stretcher bars (or stretcher frames).

http://www.amazon.com/gp/product/images/B0007LCZV4...

http://wholesaleartsframes.com/categories/Stretche...

http://en.wikipedia.org/wiki/Stretcher_bar

Apparently, a canvas is wrapped around stretcher bars if you want it to last. You can also buy very cheap canvases that are wrapped around cardboard, but they are not as good.

I did a Google search for "parts of a stretched canvas" and found the site listed below as a source. It has a lot of information on preparing your own canvas and includes illustrations.

Mount? You can also have your painting double framed, a thin plain frame inside the more ornate outer frame.

oops, sorry, I didn't read your whole question. Honey, I think that's just called the frame.