Does SSH take a different route depending on whether it's given a public or private IP?

I have an old laptop I use as an SSH server running debian. I've been accessing it a lot even when home for a bunch of things, including sending some fairly hefty stuff through a tunnel. My question is: Will sshing to 192.168.xx.xx while on the local network give me better results than pointing ssh at the public IP? If I point at the public IP while on a machine using that same IP, will the packets need to bounce off the next router down the line before coming back to me, or is my router smart enough to know to pass outgoing packets aimed at its address directly back into the local network?

Edit: Thank you everyone! Your answers were all very informative.