Should I get a leather jacket specifically made for motorcycle riding?

It depends on how thick and sturdy your old jacket is. I really recommend a full set of leathers for racing. I was wearing one on a dirt track when I went face up backwards through the air, came down on my shoulders and drifted a long way, feeling that gravel massaging my back -- they made me sit in the ambulance -- couldn't believe I was ok, but I was unscathed.

I think that they are pretty much the same. The motorbike jacket might be a little better and if you are worried you should get one, however, I don't think that it will make much of a difference. Hope this helped.