In Geometry we talked about Adjacent Angles (any two angles that share a common side) and about Linear Pairs (adjacent angles that also add up to 180 degrees). Thus we could say "All Linear Pairs are also Adjacent Angles, but not all adjacent angles are linear pairs."
If you want to talk to your student about this, try to think of other cases where one group is a subgroup of another group, so that similar statements can be made. For example:
"If someone is a football player then they are an athlete, but not all athletes play football."
"A 69 Mustang is a muscle car. I drive a muscle car but it's not a 69 Mustang."
This kind of concept is going to be central to our discussion of logic in chapter 2.
Also for every such pairing shared in the comments section of this post, your student can earn a brownie point in class. (1 point per student).