Bump maps are not always the same as normal maps. Bump maps tend to concern only the height of a pixel for lighting, while normal maps concern X, Y, and Z values for lighting.
In Source terms, the two terms are usually interchangeable as far as I know. The Parallax effect is different and comes from Parallax Mapping.
I’m not a texture guy so I’m just saying what’s off the top of my head here…

