You're very observant. There are two styles: "conventional grip", which grips the stick through the thumb and first & second fingers, with the thumb up; and "matched grip", in which both sticks are held the same, with the palm down.
Conventional grip has been around for hundreds of years. That left handed grip was developed when a drum was hung by a strap over the right shoulder across the body to march. The drum hangs at a natural angel (say 45 degrees), which would make it difficult for the drummer to hit the drum with the left hand palm down. Therefore a technique gradually developed which would allow the stick to angle down near to the same angel as the drum, thereby making it easier to play.
But when the modern snare drum stand allowed the drum to be parallel to the ground, or with the newer harness which can hold the drum flat (as with drum corps), there was no real need to use that left handed conventional grip. Still you can see pictures of early jazz drummers who adjusted the drum stand to an angle so that they could more easily use the conventional grip. And there are loads of drummers who continue to use conventional left hand grip even on a flat level snare drum, and I'm sure it continues to be taught.
However the other major disciplines in percussion instruments, such as timpani, marimba, vibraphone, and most miscellaneous percussion instruments all use matched grip. I learned to play with conventional grip, but at my first year at music conservatory it dawned on me that there was no good reason to play that way any more, so I switched. Then all percussion instruments could be played closely alike. It took me only a couple of days to become comfortable with it. After all, I had my own right hand to imitate. Later when I got back into playing the drum set, I learned that it freed me up considerably. For example most drummers play the hi-hat cymbals (which is to their left) with the right hand crossed over top of their left hand, which plays the snare drum. But with matched grip there is no need to cross over. Just play the hi-hat with the matched grip left hand.
This was a long winded answer to your question, but it does come up from time to time, and it makes sense why people would be confused.