"Regular" therapy deals with a lot of stuff, stress from work, relationships, etc., and while that may be informed by the past trauma, it is essentially focused on the here-and-now. In my experience "trauma-focused therapy" (TF-T) goes back to the past and approaches the trauma head-on. It helps you deal with the past trauma directly so you can process it and it becomes less intense in the present.
When I was doing Prolonged Exposure we only spent about 5 minutes checking in about the past week, and then everything else was about either the homework or actively processing a particular memory.
It's been my experience that there are some excellent t out there, who do "deal with" the trauma their clients have been through, but that is not the same thing as TF-T, where it is the only thing you deal with.