What is the difference between kidney beans, navy beans, and black turtle beans?

Here's a chart showing soaking and cooking times for different kinds of beans. Note that your "black turtle beans" are the same as the "black beans" on the chart.

Kidney Beans: soak 6-8 hours, simmer 60 minutes

Navy Beans: soak 6-8 hours, simmer 45-60 minutes

Black (Turtle) Beans: soak 4 hours, simmer 60-90 minutes

In practice, beans can be soaked for longer than the listed times, really as long as is convenient to you. I usually soak mine overnight on the counter if I'm sure I'll cook them the next day. If I'm not sure whether I'll get around to cooking them the next day, I soak them in the fridge and leave them there for up to several days.

Actual bean cook time can vary somewhat depending on how old the beans are. So in practice, you should expect to cook them for at least the minimum recommended time. After they've simmered for that length of time, spoon out a couple of beans and test for doneness. You can test them by biting them (if they're soft, they're cooked; if they're hard they're not). Or blow on the hot beans; the skin on cooked beans will usually crack open and roll back.

Yes, different varieties of beans taste different. Navy beans have a fairly neutral taste. Kidney beans and black turtle beans each have their own distinctive taste.