Would it make sense for me to pay off a loan with another?

I am currently in a loan period for graduate school, which has a higher apr than a previous, now consolidated loan. If I make monthly payments to my previous loan using my loans now, aren’t I making out well?

For instance, let’s say I have an 8% apr on my current loans. If they sit in my bank account, I’ll be charged 8%. But if I pay off my loans with, say a 4% apr, that means not only am I paying those down, but that I make the most out of the 8% loan by cutting the rate in half because I’m using it to fight another percentage.

Or do I have this all wrong and backward?

Help, Fluthericians.

Thanks :)

P.S. On another note – what happens if the 2nd loan is higher, then does that reverse the trend, and make it stupid to do?