Terrence Williams is happy but not satisfied. He is relieved but not relaxed.

And for a man who’s picked up mileage (and a shaky reputation) while changing teams and even countries since being drafted No. 11 overall in 2009, the distinctions are extremely important.

The Celtics have signed him for the remainder of this season and will guarantee next year if he makes the club — a giant step forward for someone who genuinely appears intent on altering his career course and changing the perceptions.

But while Williams appreciates where he has landed, he doesn’t for a minute want to take his foot off the gas pedal now that he’s driving in the proper direction.

“It’s a comfort level, but I don’t want to be too comfortable,” he said yesterday before practice and a flight to Philadelphia. “At the end of the day, my ultimate goal is not reached. I have the satisfaction that I have some type of security in my mind, but I still have to work every day.

“It’s definitely a load off to know that in the summer you know who you’re working for. You’re not thinking about trying to find a team or thinking about overseas or anything like that. You know who you’re working for.”

And who Williams is working for now seems to be having a profound effect on him. It was a given that he’d look at his next NBA opportunity differently after what was a difficult experience for him in China, but to have that chance be with one of the NBA’s cornerstone franchises has added to what he sees as a blessing.