Is There a Protagonist Character type Between a Hero and an Anti-Hero?

An example of who I am talking about would be a character who has a survivalist/realist mind -set, loves his friends,family, and personal connections but has a great distrust for the greater society at large and the authority figures in it. He doesn't want to do anything evil but he also doesn't want to do anything heroic or take unnecessary risk for the greater good of society and he also lacks leadership qualities/abilities.

If he were in a mid-evil setting he would rather stay in his village and protect it from the enemy with the other village men rather than to go war for the glory of the king and the kingdom. All of his acts are motivated to help the people he loves rather than to help his country, his authority figures, his society at large, or a list of ideals.

If he were in a modern setting, he would go into the scene of a bank robbery or mass shooting, but only to go in into it to protect his girlfriend and escort her out of the place while allowing the bad guys to do what they want to everyone else and get away with their crimes so long as they didn't go after his girlfriend.

Would this Character be a Hero, a very Light Anti-Hero, or some Other type of Protagonist?