importar vs interesar
Both follow the gustar pattern. Importar is 'to matter' or 'to mind'. Interesar is 'to be interested in'. And importar also means 'import'.
importar
To matter, to mind, or to import goods.
No me importa.
I don't mind. / It doesn't matter to me.
Not a rejection — just indifference.
¿Te importa si abro la ventana?
Do you mind if I open the window?
Polite request. Answer 'no, claro que no' to say yes.
Importan petróleo de otros países.
They import oil from other countries.
The commercial sense. Here it's a normal subject-verb structure.
interesar
To interest — the thing is the subject, you're the indirect object.
Me interesa la historia.
I'm interested in history.
The gustar pattern. History interests me.
¿Te interesan los coches?
Are you into cars?
Plural subject, plural verb.
No me interesa esa oferta.
I'm not interested in that offer.
Used for polite refusals.
Tricky bit
'¿Te importa?' with a yes/no answer trips up speakers of English. 'Do you mind?' 'No, no me importa' (I don't mind). Saying 'sí' means you do mind.