"TM stands for Technical Machine. Pokemon Trainers can give these CDs to their Pokémon to help them to learn new moves to use against opponent Pokémon. In Pokémon Generations 1-4, TM's could only be used once, and then they disappear. Recently, though, Pokémon Black and White allowed players to use them more than once, just like an HM."
Если вкратце то ТМ позволяет покемону выучить новое умение, ТМы пронумерованы, поэтому можешь погуглить таблицу с навыком, который дает тот или другой ТМ.
"The difference between a TM and an HM is most pronounced in the earlier games in the series, where TMs were single-use items while HMs could be used an unlimited amount of times after they were obtained, and unlike TMs could not be tossed or sold for money. Additionally, the moves contained within an HM cannot be forgotten by Pokémon under normal circumstances. An HM move can be used in the field by a Pokémon even if the Pokémon has fainted during battle or has run out of PP (using it in the field does not consume PP)."
HM это почти тоже самое, отличия:
HM в отличие от TM - многоразовый предмет, но его нельзя выбросить/продать
Покемон не сможет забыть полученный от HM навык (в большинстве случаев)
HM умения можно использовать в бою даже если покемон потерял сознание или не хватает PP