Yes
The film's director, Colin Trevorrow confirmed explicitly that she's the same dino seen in Jurassic Park in a few different interviews.
“The T. Rex in this movie is the same T. Rex from ‘Jurassic Park,’”
said director Colin Trevorrow, who also co-wrote the much-hyped fourth
film inspired by the work of author Michael Crichton. “She’s been on
the island for 22 years. She’s still alive. She’s a little older, and
she’s angry.”
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and
CT: The T. rex that’s in the film is the T. rex from the original Jurassic Park. She is 22 years older. But she’s not limping around.
Q. Will audiences immediately recognize that it’s the same–?
CT: I hope so. Yeah. I mean, we took the original design and obviously,
technology has changed. So, it’s going to move a little bit
differently, but it’ll move differently because it’s older. And we’re
giving her some scars and we’re tightening her skin. So, she has that
feeling of, like, an older Burt Lancaster. And this movie is her
Unforgiven.
Original T. rex Returns in ‘Jurassic World,’ This Film “Is Her Unforgiven”
and
CT: See, we do have returning characters from the first film, they just aren’t human. We have him and we have the T. rex and I consider the T. rex to be the hero of the first movie. We do bring him back.
Q. So that’s the same T. rex from the first movie?
CT: Yeah, you’ll see that the scars that the raptors gave her at the end of the first movie are still on her now.
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As did the film's 'Digital Creature Model Supervisor', Geoff Campbell
Q: Did you put any kind of effort into trying to maintain the feel of dinosaurs from previous installments of the franchise?
GC: Most of T-rex shots in the original Jurassic Park were digital models although there were the Stan Winston practical models for a number of closeup shots. But even starting from the original ILM digital model posed a number of challenges.
The first was maintaining the look and feel of the original T-rex while aging her 23 years. We didn’t have access to the original molds or castings which were all in LA but we did have a four foot original casting that had been made for us back in 1992 and which sits on display in our San Francisco studio. I made a suggestion that we scan that model as a starting point for recreating the Winston mode.
...
We now had our version to match the original Jurassic Park T-rex but we needed to age her 23 years to bring her into the present day. Tim and Glen suggested that we take into account that she’d been incarcerated in a theme park for all those years and her muscles would have atrophied somewhat. We also considered that she would be showing signs of stress, but most of all she needed to remain recognizable as the heroic, statuesque T-rex from the original movie. I think the most surprising reference we received was from Colin, who sent us shirtless images of an aging Iggy Pop wearing a pair of faded cut off blue jeans. What was interesting in that reference was the sinewy, veiny nature of his skin since he had practically zero body fat. Steve used that as his guide and did an excellent job aging T-rex while keeping her muscular and easily identifiable as the T-rex we all know and love.
Interview: ILM on Jurassic World
To back this up, the viral website site constructed to market the Jurassic World film speaks to how the T.Rex seen in Jurassic Park ("Rexy") was captured.
OWNER: HOSKINS
VIC DATE: 04/19/2002 1910 CST
SUBJECT: WEEK 3
NOTES: I WAS IMPRESSED WITH THE TEAM TODAY. HELL, STARING A SEVEN TON
PREDATOR IN THE EYES IS NO EASY JOB. THESE THINGS ARE BIGGER THAN
YOU'D EXPECT! LET'S JUST HOPE TIMACK KNOWS HOW TO BUILD STRONG
PADDOCKS.
And the film's official tie-in website article on the T.Rex confirms that the dinosaur has been on the island for 25 years (i.e. prior to the construction of Jurassic World).
T. REX KINGDOM
It's T. rex's world—the rest of us are just visiting it. Venture into
the Jurassic- sized viewing area to see the legendary predator in her
natural domain. After all, she's been living on Isla Nublar for over
twenty-five years! Feedings are scheduled every two hours.
Warning: This attraction may be too intense for children and some
adults.
It's worth noting that the visual effects modelers took the time to add scarring to the older T. Rex that matches the wounds inflicted by the raptors in the final scenes of Jurassic Park
Jurassic Park
had the island firebombed at the end, but the movie (as filmed, not looking at the script) did no such thing.