I follow Tampa Bay as my second team and I can you the Lightning didn't keep the "same core." When you see long haulers like Stamkos and Hedman and maybe Killorn, those are the last men standing from a team that evolved a lot under Yzerman and Brisebois over the past 10 years.
In net, they went from Dwayne Roloson on the Cinderella 2011 ECF run to getting Ben Bishop for Cory Conacher, who was a young up and coming winger for a brief amount of time. The next year they missed the playoffs and also traded a top 4 defenseman in Kyle Quincey to Detroit for the Andrei Vasilevskiy pick and set themselves up for two starting goalie changes over the next decade.
They also bought out Vincent Lecavalier at the age of 32-33 because his contract was just going to run forever and block them from doing anything. They traded Marty St. Louis who was still in his prime over the Olympic team selection fiasco. Maybe there's a parallel there with Tavares, maybe not, but they did make massive changes to their older core.
In terms of moving out youth, Jonathan Drouin was their highest pick since Hedman and Stamkos in 2013. They ended up trading him for Mikhail Sergachev in 2017 to improve their defense. Teddy Purcell was a roughly Zach Hyman level outer core member. They traded him.
All the while they kept getting better because they drafted Palat, Kucherov, Cirelli and Point and signed guys like Johnson and Gourde. At least two of those guys are better than Stamkos. To use a comparison we would have to be drafting guys in high volume who are in some cases as good or if not better than Matthews, Marner and Nylander.
There's no real equivalency between Toronto and Tampa Bay other than on the most superficial levels that ew both have flashy forwards and wear blue and white. Their build took a very long time, involved massive core changing moves and they had some setbacks but very early on they had a pillar on defense and a couple of blue chip options in goal. They also drafted at an unreal level which we have not done.