Are a mammogram and mammogram compression the same thing?

No. A "compression view" is a mammogram that is done, well... With extra squishing. This is done to see if an abnormality goes away when the breast is squished harder between the mammogram plates. If so, it means the abnormality was a fold of skin or overlapping tissue, not a cancer.
Yes and No. Compression of the breast is used during the mammogram to spread out the breast tissue and minimize motion. Also, there are special mammographic views called 'spot compression' views, which focus on a small region of the breast, when screening mammo identifies a potential abnormality.
Pretty much. During a mammogram, the technologist will use the machine to compress the breast flat. This is done to even out the thickness of the tissue to make it easier to visualize the tiny structures being looked for. Sometimes they will do a more focal compression for a zoom view to see something of particular interest.