If something is distinct, it is easy to tell apart from other things. Or, it is obviously separate from other things. It can also mean different, or clearly outlined.
A distinct flavour (when you taste it, you immediately know what it is. Ie. Coriander has a distinct flavour)
A distinct voice (when you hear it, you know exactly whose voice it is)
Silver is distinct from gold. (in this case, it means silver is different from gold)
On two distinct occasions. (on two separate occasions)
The ship appeared as a distinct silhouette. (the silhouette was very clear and easily identifiable as a ship)
If something is distinctive, it either helps to or serves to distinguish itself from other things.
Male salmon have a distinctive curve in their jaws. (this curve helps to identify which salmon are males / helps to distinguish males from females)
The members of the tribe had distinctive tattoos on their bodies. (the tattoos served to identify which people belonged to the tribe)
Although it is only slight, there is some difference between the two words. I hope I could help!