Hi Yoona.
These words are not the same, but they are similar.
Bezig is like ''busy'' in English in the meaning of ''busy doing something''. (Ik ben bezig Nederlands te leren - I am busy learning Dutch/I am currently learning Dutch.) (Niet storen nu, ik ben bezig met iets/ Don't disturb, I am busy doing something)
Druk is like ''busy'' of a ''busy place'', ''busy road'', ''I am busy'' (in the sense of: a person who has a lot to do). Druk can also mean crowded, or when referring to an active, lively person, like a kid with a lot of energy.
Druk and bezig are quite similar, but their use isn't the same. I hope this clarifies the difference a bit.
Bezet is a bit more different than the two words above: it's like ''occupied'', for example when a toilet is already occupied by someone before you, or when someone can't help you with something because they are helping someone else.
Hope this helps. I understand the confusion because these words have similar connotations.
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Hier nog een verbetering van je eigen zinnen:
Ik zie vaak (het woord) "bezig" wanneer ik op internet zit.
Maar ik snap de verschillen (nog) niet.