When creating a character, on top choosing a Game Mode, additional challenges can be chosen: Solo Account Found (SAF) or Solo Character Found (SCF). This is not a permanent decision and you can opt-out from challenges in options.
Solo Account Mode (SAF) characters are unable to party with nor obtain items found by other players. This also includes any items found with Solo Character Found characters even if they share the same game mode and Season. However, items found by other Solo Account Mode characters will share the stash and Item Faction progress in the same game mode and Season
All characters created in Offline are by default Solo Account Found characters, unless opted-in for Solo Character Found. You can opt-out of Solo Account Found and turn the character to just Normal or Hardcore character with no extra challenges if it's an Online character.
Solo Character Found (SCF) is an added challenge to Solo where only items found by that character can be used by it, and no stash or Item Faction progress is shared with any other characters, even by your other Solo Character Found characters. You can opt-out of Solo Account Mode and turn the character to Solo Account Found to gain access to shared progress of other Solo Account Mode characters.