The YF vaccine is a "live attenuated" vaccine, which means they give you the actual virus, but it's been "detuned" to not replicate...hopefully.
There is a very small, but non zero chance it could mutate back to a pathogenic form and you get the actual disease.
FWIW, the J&J and M/P vaccines work essentially the same way, the only difference is the delivery mechanism. The M/P use nano-particles to deliver the mRNA directly, and they're very sensitive to temperature, hence the low temp requirement. The J&J uses a viral vector (also "detuned" to not replicate) which is why it's high temperature stable. But it contains the same coding to produce the COVID proteins.
I'm not really sure why people get hyper about one or the other, since they do the same thing.