Fun-loving is just another way to say a person who likes to involve themselves in many activities and carries a positive attitude.
Living life to the fullest- is not holding back or hesitating and taking opportunities as they come. It's looking on the brighter side of things and finding the good in the unfortunate. It means you chase after your dreams, doing what you want, and giving most things your 100% effort.
The opposite of this is someone like me.
I don't go with the flow or seek out new things. I don't consider myself to be optimistic, I miss my chances, am hesitant, and don't put in as much effort.
Fun-loving doesn't mean literally, it's more of a positive attitude towards life.