Equivalent of SDL_BlitSurface in OpenGL?

I was planning to have 2 textures in my application; one for the main
display and one for the font data. But I found that since the texture
itself is big enough to hold both (because of power or 2 requirements),
then I can use the one main texture.

My question is, what is the equivalent OpenGL command (when working with
textures) for the following SDL code?

SDL_Rect srcrect, dstrect;
// rects are filled with correct coordinates
SDL_BlitSurface(texture_surface, &srcrect, texture_surface, &dstrect);

I assume that it will use glCopyTexSubImage2D(). Also, when I overlay the
font subtexture, I’d like to to take into account the alpha-levels
defined in the font subtexture.