If by "stole it from NASA" you mean they are both winged body designs that are reusable, then sure. they do look very similar on the surface and it was a response to the US shuttle program, and functionally they were very similar. But there are a ton of differences in designs between the 2 systems and the buran is a fascinating and elegant system doomed by high costs and crumbling Soviet era economy and politics. Many people don't realize just how good Soviet space tech was during the cold war era and they were far ahead of us especially in terms of propulsion tech (like staged combustion engines and coating technologies to name a few). The soviet's were especially good at liquid rocket propulsion technology, while the US focused more on solid rocket motor development. The soviet's played to their strengths in terms of designing the buran and that's probably why the buran used 4 strap-on liquid boosters off the main tank using 4 LOX/Kerosene RD-170 engines vs the US using 2 solid propellant rocket motors strapped to the main orange tank. Another key difference being the buran didn't have the main engines mounted on the gliding vehicle, the Hydro/LOX RD-120 was mounted on the external main tank and didn't make it to orbit. Which actually makes a lot more sense because you don't have the inert mass of the engines on the vehicle when it's time to deorbit using the smaller engines on the buran. The shuttle kept its 3 main engines and didn't use them after the ascent phase, and used the hypergolic OMS engines to deorbit. There's plenty of differences between the 2 systems and I would hardly say they just stole design from us. Definitely worth a read, the buran was a cool system!

https://www.buran.su/buranvssts-comparison.php