It's a totally reasonable thing to be confused about. I was baptized at a Catholic parish as a child and I only relatively recently learned of the existence of many other rites besides the Latin one. Here[1] is an article by a canonist going into some detail. The short version is there are many churches in full communion with Rome that retain their own traditions, including married priests. Theoretically even a Latin rite priest could have the discipline of celibacy dispensed, but I've never even heard of that actually happening. I wouldn't be gobsmacked if it has though.

[1] https://canonlawmadeeasy.wordpress.com/2007/09/20/are-they-r...