Dear Hicham, COSY is a 2D spectrum that shows scalar coupling between vicinal H atoms (via 3 bonds). On both axis you have 1H spectrum and you can see the exact correlations and it can help you resolve structure. HSQC on the other hand shows correlation between C and H that is bonded to it (via 1 bond). On one axis you have 13C or DEPT, on the other 1H spectrum. Both of these spectra are very powerful, especially when combined for determination of the structures of small organic molecules. The biggest limitation is molecule size and for big molecules that are not symmetrical, it can be hard to see correlations because they can overlap.

Thank you very much dear @Ivana Jevtic , for your complete answer.

Dear Hicham, I only want to add that using HSQC you can get not only correlation between C and H but with any heteroatom (e.g. 31P, 14N, 17F)

dear V. M. Anishchenko , is it necessary to couple a 13C, 31P, 14N or 17F NMR with proton when doing HSQC, or you can correlate between 13C, 31P, 14N, 17F data directly, kind regards

Using HSQC you can't obtain a correlation between two heteroatoms. Basically HSQC involves the transfer of magnetization on the proton to the second nucleus. So one axis should be 1H.

14N nuclei are non-magnetic and don't use in NMR. This is my mistake. 15N is used

thank you very much for your complete answer dear V. M. Anishchenko