There are many example but some are on the same show 2 examples are The "V" shaped alien craft in alien hunters appearing as a space ship in the show "The Universe." Another example is the Star Trek earth space port appearing in the "Life after Humans" and "The Universe" again.
Simple answer: those bits of footage were used as stock footage shots (the Star Trek 2nd unit model footage for instance).
The major studios often lease out their sci-fi and action movie chase/stunt sequence related footage as stock footage to other producers (one example: a B-movie reusing spacecraft shots from the original Battlestar Galactica).