As has already been said, parting tools come in all sorts of shapes and sizes. My personal favourite is a 10mm beading and parting tool which I also use like a skew, so for me, it is a perfect turners chisel.
One problem I feel I should point out is that if you simply make a cut with any parting tool, cutting in the obvious way, the edge next to the cut might be straight and square but it will be very rough, well beyond anything sanding will repair, so you will need to make a slicing cut either with a skew or the beading and parting tool will also do it. This involves cutting with the tip or point of the tool with the bevel rubbing/gliding behind the cut.
Hope this helps and makes sense.
Edit, the above refers to spindle turning only! For bowls, stick to a bowl gouge