Can интересно and интересовать/ся be used interchangeably, or do they have a somewhat different meanings? I know that these are different words and that интересовать is a verb, so I am asking specifically about usage here.
In other words, can вам интересен be used in the same way as вы интересуетесь?
Thank you!
интересоваться, being a verb implies active action on the part of the subject and being imperfective implies some history of being actively interested in something. интересно is a passive construction and so may mean just a momentary curiosity (though it doesn't exclude active interest).
If the words mean an object of curiosity, вам интересен .. ? means is it interesting to you and вы интересуетесь means something like do you have a hobby/professional interest.
If the meaning is that of 'benefit', you would ask вам интересен if you're offering a deal to an unsuspecting customer (i.e. hoping to incite an interest) and вы интересуетесь is what e.g. a sales assistant in a shop would ask, seeing that the customer is already in active search for something.
So, вам интересен is asking about the person's reaction to the (grammatical) subject and вы интересуетесь is asking about the person's objects of interest.
The difference is pretty much the same as between English "to be interested (in)" and "to take interest in": the latter implies active effort in learning new things about the object of interest.
Ему интересно рисование means "he's interested in drawing". When there's Bob Ross' show on TV, he stays tuned, and when he's bored, he can sketch a cat.
Он интересуется рисованием means "he takes interest in drawing". He's taking online courses, doing research and spending his time improving his drawing technique.
In reality these both words are interchangeable. It almost entirely depends on the idea you want to add up to the conversation in terms of the situation being implied. Он интересуется теннисом (фотографией)/Ему интересен теннис (интересна фотография) - He may either watch broadcasts on tennis (photography) or take up, practice tennis (photography) or manage tennis cups (photo exhibitions). Он интересуется акциями (выпуском акций)/Ему интересны акции (интересен выпуск акций) - He can read about shares (share issuance) as well as trade shares (issue shares). Он интересуется рыбой/Ему интересна рыба-either of these variants can allude to his being interested in cooking or trading or breeding fish or even studying ihtiology. In some cases you will need to use an adjunct to avoid ambiguity: Он интересуется только деревообработкой/Ему интересна только деревообработка - the situation in focus can refer both to his being in the wood-working business or studying the issues of the processing of wood or he may even teach this as a subject at the institute. For example, you are speaking of your friend who works in a woodworking enterprise to some other person and he asks: "What job is your friend doing there, is he managing selling timber?", you may answer: "Он интересуется только деревообработкой/Ему интересна только деревообработка" (He interests himself only in the processing of wood/It is only wood-processing which interests him).
