When Doctor Strange uses the Time Stone, he is clearly using a spell, being that he learns how to use it from a spell book, and that it has runes and a pentagram, reminiscent of his normal orange spells. Presumably the spell draws energy from the Time Stone instead of the "dimensional energy" used in regular spells. Thanos on the other hand, doesn't use magic, so why when he uses the Time Stone does it manifest like a spell rather than just closing his fist and time turning back?
TL:DR we simply don't know yet, it may have some relevance in the next film.
In the comics, Thanos is also a master of the mystic arts (aliens have wizards, too). It's unclear whether this has transferred to the films or not. However, Thanos has displayed the ability to simply punch the mirror dimension and can, in other ways, keep up with Doctor Strange in their fight in Avengers: Infinity War, which does seem to imply that he has at least some understanding of the mystic arts. The only lines we have in relation to this, in terms of the Marvel Cinematic Universe, is this from the wiki:
He was able to be far more capable and familiar in using the Time Stone's powers than Doctor Strange.
Your powers are quaint, you must be popular with children.
Which would seem to suggest Strange's style of mystic arts are at least understood (and perhaps surpassed) by aliens. In which case, Thanos would have learned at least how to use the time stone at some point in the thousands of years that he's been searching for it.
Another option is that the green runes are inherent to the Time Stone, and that Strange's (and indeed, all of the Kamar Taj's) orange runes are, in turn, based off of the Time Stone. This isn't without precedent, as there is a very popular fan-theory that the function of the ARC reactor is based somewhat upon the Tesseract. It would also explain how such powerful sorcery found its way to Earth: Agamotto built, or found, the Eye of Agamotto and used the Time Stone to discover and learn how to wield dimensional energy.
There are other possibilities, most notably that Doctor Strange is still acting through the Time Stone somehow, possibly by means of a curse. However, we obviously won't know if this is true until the next Avengers film.
No interviews from Avengers cast members or crew have been made that discuss this (to my knowledge, if I'm wrong, please do say). So really, it's all up to you and your head-canon until then.
Sorry, a more satisfactory answer cannot be achieved yet.