My question is specifically about Akila Dananjaya. He is termed as an off spinner. Yet I have seen some videos in which commentators quote few of his deliveries as 'Googly'. But, Googly is type of delivery used by Wrist spinners right? Also it rotates inward to a right handed batsmen (clockwise), so if any off spinner bowls such delivery, shouldn't it be called regular off spin delivery?
To quote from the very Cricinfo page you link to:
Another installment from Sri Lanka's production line of unorthodox spinners [...] Able to deliver a legbreak, googly, carrom ball, doosra and a stock offspinner
Dananjaya is both a finger spinner and a wrist spinner, so he has (at least) two balls which turn into the right-handed batsman: the standard offspinner, bowled with a finger spinner's action, and the googly, bowled with a wrist spinner's action. Similarly, he can bowl two balls which turn away from the right-hander: the regular legbreak and the doosra.
The large selection of variations than Dananjaya possesses makes it harder for a batsman to read - for example, if a bowler can bowl only legbreaks and googlies, it's relatively easy to read the bowler from the hand by noting whether the back of the hand is facing the batsman or not. But with Dananjaya, the "back of the hand" ball could equally well be the doosra turning away from the right-hander, as opposed to the googly turning into the right hander.