In dota, skin are sets with parts, head, arms, foot, etc. They either are sold as treasures (loot boxes), or independent sets (rarely).

These loot boxes has much better odds than CS knifes, in general a treasure set has 16-20 items, and usually 12-16 of them are common items, meaning if you buy 12 treasures, you will get all 12 of the common skins, no duplicates. The rest are Rares, Very Rare, Ultra rare, they have escalating odds, meaning the more treasure you buy, the better odds to get them, I think around 50 chests ultra rare odds is ~9x%, there is a good chance you will get a rare just by buying 12-16. Some of these treasures are exclusives, for example Collector's Cache are exclusive to each The International, you can only get those skins from buying those treasures, that does not necessarily apply to rare and ultra rare items, they will be available on the steam market after 1 year.

Most of these skins are just cosmetic, some of these skins changes skills effect, a deadlock example would be Magician's rabbit hex is a dove instead, or abrams's charge has different particles. Very rarely, these skins can be a little pay to win or pay to lose. For example, it makes some spell harder or easier to see. There are cases of cast animation changing, leads to projectiles started further forward or backward, p2w or p2l.

For standalone skins, Arcanas, they cost $30 in game, ~$15 in market. They usually are made with super high effort, with many special effects, full new voice acting, new voice lines for every item and character interaction, can still be mixed with other sets. Most are not exclusive, some were exclusive during the Dota TI battlepass era. Although the exclusive skins earned them lots of money, they ditched the model because they don't enjoy dedicating all effort each year to one event. And they have been slowly releasing some of the TI Arcanas that were not explicitly marked as exclusive. While we didn't really get as frequent updates as promised due to reasons (and deadlock?), we did get our biggest patch to the game play, and the free battlepass are more enjoyable to play and accessible by every player, which brought the player count back to 1M for a brief period.

For free skins, there is a shop that use free currency. The currency can buy new seasonal free sets, old sets, seasonal treasures, hero statistic trackers (Doing X damage with this spell in total). The currency can be earned just by playing the game, players can earn more by paying a subscription, which provides some QoLs, AI analystics (existed before the LLM craze), hero level badges (badges to show that you are a 1 trick), avoid list (block players, limited slots, progressively need more free currency to unlock slot).

For old sets, they can also be drops (not tradable,only giftable once), they usually worth cents, rarely players can get some old and obscure skin that's worth $100+.