On the surface, the Terminator franchise and The Abyss aren't directly related, but subtle Easter eggs connect the James Cameron movies together. Of course, linking one's films via references only fans would notice is by no means a practice exclusive to Cameron. James Wan has done things like put the Annabelle doll in Aquaman and Billy the Puppet from Saw in Insidious. Blade Runner repeats a computer program screen from Ridley Scott's prior film Alien. And so on, and so forth.
It's a fun little thing for directors to do as a nod to those familiar with their past work, but in the age of shared universes, one wonders, do these Easter eggs actually infer that a particular director might have their own shared universe of movies? If anyone were to do so, it would make sense it would be Cameron, who has a very recognizable style that makes itself apparent in all his films, no matter how disparate the individual plots might be.
A shared universe connection is definitely not readily apparent between Cameron's Terminator movies and his 1989 underwater thriller The Abyss, but if one looks hard enough, small connections become apparent. Connections that, in the universe of the movies, can only really be explained by saying they share a universe.
How The Terminator Franchise Connects to The Abyss
The first instance of an apparent Terminator and Abyss crossover dates back to 1984's original Terminator film, James Cameron's first big hit as a director. In the film, actor, stuntman, game show host, commercial pitchman, and all around Hollywood jack of all trades Joe Farago plays a TV anchorman called just that, TV Anchorman, in the credits. Farago appears in the same capacity in The Abyss, this time credited simply as Anchorman. Since he isn't given a proper name in either film, the logical conclusion is that Farago is playing the same character in both.
Additionally, and more conclusively, the oil company that owns the Deep Core drilling platform on which the events of The Abyss take place is called Benthic Petroleum, and has a distinctive logo. In Terminator 2: Judgment Day, when Sarah, John, and the T-800 hole up at a gas station after a night of being pursued by the T-1000, the gas pumps have the Benthic Petroleum logo plastered on them. There's no real reason why this can't mean that Terminator and The Abyss are set in the same universe, as nothing in the films really contradicts each other. Amusingly, Benthic ended up becoming the name of a real oil drilling company later on, although presumably their drilling rigs aren't visited by aliens.