What does it mean if I think of someone of the same gender quite a lot but when that person touch me and is near me my heart doesn’t race?

This can mean a lot of things and, unfortunately, you're the only one who can really figure it out. Some of the possibilities are: You could just really enjoy this person and not be interested in them romantically or sexually - you can have someone on your mind a lot in a completely platonic manner. You could be attracted to them romantically, but not sexually. Read up a little on what it means to be homoromantic and see if that sounds like how you feel for this person. If you are only romantically interested in a person, in short, it essentially means you are interested in someone in a way that is more than platonic, but not necessarily in a sexual way. You could definitely be sexually attracted to this person and just not be the kind of person who's heart races at physical touch! That's definitely a legitimate way to react to someone you're interested and doesn't necessarily determine your feelings towards them. In the end, these things can basically mean anything. If I were in your shoes, I would seriously think about what kind of relationship I wanted from this person. A friend? A romantic partner? A sexual partner? Something different entirely? I think once you determine how you want to be involved with this person, you can make the next steps of seeing if they'd be interested in the same kind of relationship.

It could mean several different things. 1. You could have found a really good friend and want to spend a lot of time with them. 2. You could be Ace. You don't experience sexual attraction but you've found a person you want to platonically live with for the rest of your life. Basically, a non-sexual soulmate. 3. You could be Demi-sexual. In other words, you form a deep bond with someone before you have sexual attraction. There are plenty of other reasons and I encourage you to explore all the possibilities before trying to cram yourself into a box. You don't have to know who you are just yet. Take your time and have fun discovering it!

everyone experience attraction in a different manner so your heart not racing might not mean you are not attracted or interested in the person. Also you didn't specify what kind of thoughts. You might simply be quite emotionally attached to this person, in a platonic sense. If your thoughts are more romantic or sexual then it might mean that you are attracted (sexually or romantically, or both! )or curious about the same gender and that is completely fine.