I believe that your chili peppers and banana peppers cross pollinated and created a hybrid but more like a chili peppers.

Yes they are most likely a cross.

I think the majority of pepper seed sold is for hybrid plants, and even if you buy some open pollinated varieties, peppers are largely pollinated by insects, so crossing instead of self-pollinating is very likely.

If you want to save any pepper seeds, you need to separate your different varieties by great distances.

Self pollinating and bagging the blooms would be the best way to keep seeds true. Even at great distance the chances of a cross is very possible.

Please correct me if I'm wrong:

I agree with others that your peppers were crossed. Which means the "cross pollination" took place before you received the peppers from whoever gave them to you. That person probably grew the chili and banana nearby to each other and their pollen got crossed. The cross pollination does not affect the fruit of the same year (the fruit you received last year). However, seeds in those fruit will not grow into fruit identical to the fruit it was in. I think whatever went wrong didn't happen under your supervision.
Starting peeper from seeds of unknown origin is always adventurous. You never know what you might be getting. Buying seeds is one of the more guaranteed ways of getting pepper seeds.

Peppers of any type are usable in one way or another. Just go ahead and grow them. When they are big enough assess them for heat, wall thickness etc. and use them accordingly. Crosses can often bring unexpectedly great results.