What do InsertDE, UpdateDE, UpsertDE, DeleteDE, and ClaimRow return in AMPscript?

These AMPscript functions manipulate data extension records at send time (and on CloudPages):
InsertDE("DE", col1, val1, ...) — inserts a new row; returns 1 on success.
UpdateDE("DE", numMatchCols, matchCol, matchVal, updateCol, updateVal, ...) — updates matching rows; returns the number of rows updated.
UpsertDE("DE", numMatchCols, matchCol, matchVal, col, val, ...) — inserts or updates based on match; returns 1 for insert, number of rows updated for update.
DeleteDE("DE", numMatchCols, matchCol, matchVal) — deletes matching rows; returns the count of deleted rows.
ClaimRow("DE", returnCol, matchCol, matchVal) — atomically reserves a row (sets a flag) and returns the value of the specified column; used for one-time code distribution to prevent duplicate claims.