After Terminator 2:Judgement day directed by James Cameron, came many other Terminator movies like Terminator 3, Terminator Salvation, Terminator Genisys. All these new Terminator movies' stories are different from each other and they weren't directed by James Cameron. So my question is why James Cameron didn't direct any more Terminator Movies. Did he sell his rights to some other company?
There are two reasons. Both are discussed in this article about Cameron and the Terminator franchise
The first is that he says he's creatively finished with the franchise.
I've moved on creatively from The Terminator, so I'm not really interested in that imagery and even those ideas anymore - and I'm not sure the world is that interested either. It's run its course, I feel... [Arnold Schwarzenegger's] persona was part of The Terminator and when you uncouple those, you get Terminator Salvation, which is actually a fine film from a pure filmmaking standpoint - it just doesn't gel up into anything mind-blowing... I wish I hadn't sold the rights for one dollar.
The second is that he sold the rights to the Terminator franchise back in the 80's. Explained in this article from the Toronto Sun
"I wish I hadn't sold the rights for one dollar," Cameron says, referring to a deal he struck in exchange for the chance to direct the 1984 original.
Since then, the rights have been bought and sold a few times. This means that even if he's not interested, the studio can go ahead and make more movies, as they have done.
The Terminator wiki, makes the unsourced claim (I'll keep looking later today) that Cameron was asked to do Terminator 3, but turned it down.
Schwarzenegger initially refused to star in Terminator 3 because James Cameron, who created the character and directed the first two films, would not be directing the third installment. Schwarzenegger tried to persuade Cameron to produce the third film. Cameron declined, however, and feeling that the Terminator character was as much Schwarzenegger's as it was his own, he advised Schwarzenegger to just do the third film, and ask for "nothing less than $30 million."