"Does that mean if a rifle has what has been described herein as a "magazine", the magazine fits into the magazine?"
No. In a rifle with a detachable magazine such as the Remington 522, the magazine fits into the magazine housing.
When you remove the magazine from the rifle, it no longer has a magazine.
A rifle like the Springfield 1903A3 or M1917 Enfield has an internal, non-detachable magazine, which can be loaded either with single rounds or by use of a stripper clip.