Continuity Change

Continuity Change AUs, or Concept Change AUs, are AUs that modify the continuity of Undertale or, in the case of AUs of AUs, the base-AU in some fashion. Whether the AU takes place before the main story of Undertale, during the same time-period, or after—so long as the AU doesn't qualify for any other AU Type—they're all Continuity Change AUs. AUs that place the world of Undertale into the continuity of another IP (such as EarthBound) are also Continuity Changes.

Backstory

Backstory AUs are AUs that take place before the events of Undertale or, in the case of AUs of AUs, before the story of the base-AU, but don't change anything that would happen in Undertale/the base-AU.

The timeframe of a Backstory AU can proceed to continue throughout Undertale's or the base AU's events, as long as it does not conflict with anything that happens in the story.

Special Event

Special Event AUs are AUs that change the plot of Undertale or, in the case of AUs of AUs, the base-AU in some fashion, generally through a special event that occurs that otherwise wouldn't happen. Whether this sudden change happens before the main character (Frisk in Undertale) enters the Underground or while the main character is in the Underground, both are Special Events.

Sequel

Sequel AUs are AUs that take place after the main story of Undertale or, in the case of AUs of AUs, after the story of the base-AU.

Crossworld

Crossworld AUs are AUs that place the world of Undertale or, in the case of AUs of AUs, the base-AU (whether it be the characters or the entire setting) into the world of another Intellectual Property (such as EarthBound or Pokémon), or place characters from another Intellectual Property into the world of Undertale.