"accident on the job" and "accident at work" mean about the same thing - an accident which occurred while working. One thing to be aware of: on American TV, being "on the job" means being a police officer. I don't know if that actually is true in reality.
Usually, things happen "at work" rather than "on the job".
In UK English, we'd usually say "at work" rather than "on the job". The latter used to be the customary idiom, but it was appropriated long ago as a cheeky, very British euphemism for being engaged in sexual congress, as in "I walked in while they were on the job", or "he died on the job". So, now to say "I had an accident on the job" in the UK would arouse giggles, smiles, or funny looks. The phrase featured in the titles of several porn movies from the 1970s (e.g., "Nurses on the Job").