English is my first language - and "tall" is not restricted to people. "Tall" means higher than average. Anything can be "tall". "High" means a long way above ground level.
"The high building" is a building up a mountain. You are in the city - you look into the hills - at the top of the hill - but only one storey high - is the hospital. It is a high building. But is there are lots of buildings and one stands out as being higher than the rest - that is a tall building.
Thanks you very much for your answer and of course I accept it, but in a way I think the main point should be to correct what is really wrong in the writing, or in the translation of the Hungarian language and not this kind of "wrong" translation to English which to me seems pretty picky because "tall" and "high" both have pretty much the same meaning. It's just a matter of nuance.
I speak New Zealand English which is basically UK English with Maori words. I also read US English books. I assure you "tall building" is common.
The definition I gave earlier for tall and high paraphrases the Shorter Oxford English Dictionary which is the reference for UK English.
Neither do I. But even though I think it feels weird to say "a tall building" and if I believe I speak fluent English, I must accept that I never can compare myself to a native, up to a certain limit.
In French, which is my native language, one would say that a building is high (haut) not "tall" (long, élevé). Maybe that's why "a tall building" sounds weird to me.
I think that was just a sort-of-useful approximation. What's important is to not use "high" by itself for people unless you mean they are under the effects of (illegal, generally) drugs. As a native English speaker, "high" is not used to describe heights of things. It's used for "elevations," above either the ground, floor, or sea level depending on context.