Don't think that's quite right, TOPS-20 was actually a fork of the Tenex code and so was pretty similar. Not sure what the relationship with TOPS-10 was.
TENEX started out as modification of TOPS-10 code base, afaik due to expanding needs leading BBN to create both TENEX and custom pager addon to PDP-10. Some time later DEC acquired TENEX code, cut it down some, modified some, and released it with support for the official DEC pager included in later PDP-10 models
At USC we ran TOPS-10 on the student machines and TENEX, and then later, TOPS-20, in the engineering computer lab. The TOPS-20 migration allowed us to run some accounting package from the student side on the staff side. That helped mitigate some of the impact on response time on the student side which was really poor with a couple hundred students logged in at the same time.