Companion Monsters are the ones that you select from your friends. You may select 1 monster from their current team. This is a great way to benefit from different builds that others are working on. This also allows you to test out other Monsters before deciding to pursue their evolutions.
Seeing the Stats from Companion Monsters[]
If you click-hold on a Companion Monster's portrait you can see their HP/ATK/Rest stats along with their skill and their Skill Timer.