Game Modes and Leagues
In Path of Exile 2, there are four base game modes confirmed: Standard, Hardcore, Solo Self Found (SSF), and Hardcore SSF (HCSSF). Here's a brief overview of Path of exile currency each:

Standard: The base game mode with no additional rules.
Hardcore: Similar to Standard, but your character moves to Standard upon death.
SSF: No trading or playing with other players; all items are self-found.
HCSSF: A combination of Hardcore and SSF.
Additionally, there's the Ruthless mode, a PoE1 game mode that increases difficulty and reduces drop rates.

Challenge Leagues
Path of Exile features seasonal content releases known as Leagues. These leagues introduce new game modes and features, offering a fresh experience for players. Leagues are temporary and provide an opportunity for everyone to start anew. At the end of a league, characters migrate to POE currency buy their respective eternal game modes.