When you have feelings for someone, does it mean that you love the person?

Not necessarily.

Love means different things to different people, so it's difficult to define or quantify things like this - but being "in love" is universally regarded as the highest form of affectionate feeling you could have for someone.

"Having feelings" would suggest that full-blown love hasn't blossomed yet, but could do if these feelings are nurtured and allowed to develop.