Simply put: Not the same universe (storytelling or physical), just similar terminology (which appears in other Herbert books without explanation). I think this was a convention that Herbert used in his writing.
Complicated version (in universe):
Ship explained that it went to many different universes to pick up humans, and those humans came from many different points in their histories. this was in the early chapter of Jesus Incident when Raja Flattery is reviving from hybernation.
Those humans brought many things with them and it seems that ship limited access to only a small set of technologies. (referenced through out the book) - so by random chance Lasguns appeared.
Out of Universe:
Ship itself is technology far advanced over anything made by the Synchronized Worlds (for those who accept the prequels), Ix, or even Dune Encyclopedia. Omnius and Erasamus were nothing like as sophisticated as Ship. We might consider them to be the antithesis of Ship.
e-Clone technology was primitive compared to Tleilaxu bio-tech. The "axolotl tanks" refer to the same animal but that is where the comparison ends. The attitude towards the technology was completely different.
No alien intelligence appears in Dune at any point. The only alien biology in Dune is the sand-worms, which remains unexplained to this day. (and may not be alien)
Herbert uses Ship and Muad-Dib/Leto II to explore similar topics in human development and technology. One is about a god-like computer, the other about a god-like superhuman.