In looking up the meanings of these terms, they seem to be pretty much the same per Webster. But to me there is a different emotional attachment for companionship. To me companionship requires a heartfelt emotional connection between to bodies. The bodies can be the same specie or different specie. The animal world is forever showing us this emotional connection of companionship in various ways.
People can have many friends but only a few they call true friends or companions that they can share heart felt concerns, fears, joys or tears. We have drinking buddies or ice cream buddies who will hear all of our concerns and just nod at appropriate times to assure us it will be OK. Then they lock away that information and never dare share it. Loyal companions. We all need them. Man has to have someone or something to talk to. Remember the movie with Tom Hanks, Cast Away. He cut his hand and with his blood made a face on a soccer ball and called him Wilson, because that was who made the ball. God made us to have companions.
Mine sits beside me on the sofa as I type, sometime snoring loudly.
But she listens to every word, gets very concerned when my voice get upset then comes and stands protectively across my lap. It makes football very difficult to watch.
What or whoever is your companion is cherish that companionship. They really are few and far between in our lives and most needed. And companionship requires kindness, sometimes extra kindness, so remember to be kind. While your companion may out of hurt be unkind, do not return in favor. Show your inner strength and be strong and kind.