Leggings are the thinnest - personally I'm only happy wearing those with tunics/long tops in summer, except maybe round the house. For now, they're too cold and lightweight looking.
But there are some thicker leggings-type 'bottoms'. My personal favourite, if i want something that's thicker and more trouser-like than leggings, but not jeans-like, are these - thick Ponte jersey which are quite warm, and can be worn with winter tunics when thin leggings would look silly:
www.boden.co.uk/en-GB/Womens-Trousers-Jeans/WT045/Womens-Roma-Trouser.html
Treggings can be all sorts of things - it is confusing, I agree. Different retailers use it different ways. I think the ones in M and S on the whole look like thinner, less good quality, jeggings (see below).
Jeggings look like close-fitting skinny jeans but in a thinner material (usually - as someone has said, there are cord ones in M and S but these are pretty thin) and, again usually, are cheaper than jeans.
M and S jeggings have loads of fans on here - there's a long recent thread. I don't like them personally, because i have a large body and long slim legs and anything that fits me round the hips looks unflatteringly baggy on the legs. Also, at my age and size, I prefer to spend the money on one pair of good quality skinny jeans than several pairs of M and S jeggings.
But that's just me. I'm sure lots of people look great in them and they'd be worth you at least trying next to see if you like them.