There are not different kinds of adultery. It is fascinating to me that by the time of King David, it seemed that at least some of the penalties for breaking the Law were not enforced. David should have been killed for two crimes, adultery and murder. Yet God let him escape. Even in the OT, mercy prevailed over justice. And it was Bathsheba's son who ascended to the throne.
Having said all that, God also knows the motivations of the heart. The true hardliners say that the divorced should never remarry. I do not believe that God punishes the innocent along with the guilty. And adultery is not the unforgiveable sin. What man has never looked at a woman without lust? Not all women are innocent in this regard either, especially in the western world.
It's a vexed issue that I know too well myself. I was divorced in 1995 and I remarried last year. It helps to remember that God forgets when He forgives. That is not a licence to sin, but it is grace to get our lives back on the right track. Hopefully, we learn from our failures and so do not repeat them.