> If I want to invite you to a party like that, are we not friends

Acquaintances or good acquaintances.

I think this boils down to each person's definition of friends and friendship along with the amount of social interaction each person needs.

I need very little social interaction, so I tend to keep close friends and not much else. I know others who always like to be around someone. They don't care much who it is, and they generally have looser terms for friendship.

Also, face-to-face isn't required. Hop on discord or skype, or just send them a text message. If they are a close friend and you enjoy their company, you should try to keep the lines of communication open.