In principal, viral vector vaccines are technically transmissible, though I do not think we have demonstrated actual transmission anywhere. The J&J vaccine is a viral vector vaccine.

The mRNA COVID vaccines are not; with those, the vaccine material is mRNA that your body codes into a protein recognizable to the immune system. The mRNA is both unstable (so it doesn't last long inside the body) and not capable of contagious transmission

There is open research, such as https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5777272/, as to whether making intentionally transmissible vaccines is feasible (or even a good idea)