Correct. The LW20 has a short tang, like an 870. They can readily be identified in the 20ga model because the ejection port is a pure oval. Both the upper and lower edges are parallel to each other.
The LT20 has a long tang, and the ejection port swoops up in the upper rear for shell base clearance.
It is possible to have LT20 barrels machined down to fit the LW20. Some gunsmiths used to offer this service.
Also keep in mind there is a "standard" 20 ga built on the 12ga 1100 frame. These were discontinued when the LW20 came out.