Saw Teeth

I’m currently building my own stick right now and i underestimated the difficulty of it =\ cutting 45 degree angles are a pain in the ass

So my table saw’s blade is a 10in and has 40 teeth but the teeth are way to thick (1/8"). i’m taking a look at home depot and rona and there are other saws that have like 60-90 teeth.

I know the more teeth there are, the smoother the cut but it could also burn the wood (due to slower cut) and the less teeth there are, the faster the cut but it isn’t as smooth.

My question is, with more teeth, is the thickness of the teeth smaller? Or is the size of the blade the determining factor of the thickness of the teeth?