Fish do have blood, and it is red like in red meat because it contains hemoglobin.

If you cut a freshly-caught fish near major blood vessels, you will see red blood. But if the fish is old (i.e. store-bought), the blood may have coagulated, or the store may have drained out the blood during the beheading and gutting processes. In fillets, the blood vessels are sometimes so small that it is hard to see blood.

Fish do have blood. You can see it in the gills of a live fish, which are red because of it. I don't know why cooked fish do not obviously have blood the way that red meat does, but I suspect that it has more to do with how it is cooked than whether blood exists. For example, birds have blood, too, but you don't normally see blood when you cook a chicken.