The DC hierarchy goes something like: TM-> Department OM (Some of us still us the the old terminology, GL, so a GL=OM) ->Senior OM ->General Manager, who's the top dog in the DC. Past this point, I am unsure, but I think there's a Region OM and a Group OM then it's upper-level corporate HQ positions out of MN, I think.
I guess the best way to think about it is a OM=TL, SOM=ETL, and GM=STL. However, the OM's are salaried, unlike TL's, and the pay overall in the DC is higher. This is all hearsay, but a new OM makes somewhere around 60k, a SOM in the upper 5-to-low 6 figures and GM is a 6-figure position. Again all hearsay and rumor, unless someone can correct me.
Your average OM usually has a lot more on their plate than a TL, constantly coordinating with other OM's, SOM and the GM, information form HQ and outside the building, and various TMs in the building in order to keep the building running. Unlike the store, your OM doesn't usually get physically involved in the TM DC workload (like how a BRTL might do cafs or a HLTL pushing and zoning), though some will on occasion, but it's not an expectation to do so. Depending on the OM's style, a TM may or may not see their OM all that much during the shift, so in this manner, an OM may seem more like a store-side ETL than anything else. Similarly, depending on your key, a TM may go quite a while before ever seeing their SOM on the floor.
There are a few other salaried positions in the DC, including the HRBP, who are sorta like OM's of the HR techs, and deal with bigger HR issues, and their boss which I think is the HRM. There's also the PC's (Production Controller) who make both daily and long-term staffing decisions thoughout the DC dept's.
I'm just a TM, so there's probably stuff I'm missing or incorrect on, but that should give you a good start.