Both of these adverbs mean “with regret” but in very different ways.
Regretfully means that the action of the verb is performed with regret; i.e., the person acting wishes they did not perform their action:
We regretfully said goodbye to our friends.
Regrettably (regret-able-ly) means that the action could and should be regretted (by anyone) – but not necessarily by the person performing the action:
Regrettably, Putin invaded Ukraine today, but I don’t think he regrets it.