Underwear is a preference.
Some like thongs, others boyshorts. Then there is bikini cut, briefs, and the list goes on! For me what I wear casually and what I wear to work out varies too. I want to be comfortable when I have my legs flipped over my head in plough position. At the same time I don't really feel like flashin' my pantyline to everyone either. Bend, stretch, pivot and there goes my underwear! Riding up where I don't want it to. Surrounded by a room full of people, it is a little tricky to subtly "adjust" underwear back into place. So getting the right fit and function for what you are doing is important.
I love our thongs at lululemon! In particular it is the thick side bands that I adore, which are super comfy and don't dig in. And for when you are getting your sweat on they even have technical underwear that is moisture wicking.
When it comes to a yoga class, I go for something entirely different. The featherlight boyshort is perfect for any kind of yoga class. Super silky, super thin and light and - most importantly - flat seamed! When I wear this underwear there is no need to worry about it wedging or bunching in all the wrong places and only has a subtle pantyline under my tight Groove Pants. In fact all of lululemon's underwear, like our technical clothing, has flat seams.
Next workout, take a second to think about what's under your yogawear.