They are technically different. Mixed episodes aka dysphoric mania.

Rapid cycling has the same episodes - mania and depression- just they cycle much faster.

But for me it gets blurry. I know for a fact that my episodes cycle in 2 weeks. So if it feels like im rapid cycling, then Im probably in a mixed state. Bc my mixed episodes look either like classic dysphoric mania or very rapid mood changes (sad to happy to angry)