OALD:
phrasal verb ,hold 'on
1 (informal) used to tell sb to wait or stop syn wait: Hold on a minute while I get my breath back. * Hold on! This isn’t the right road.
American Heritage:
hang on 4. To wait for a short period of time.
hold on 3. To wait for something wanted or requested, especially to keep a telephone connection open.
M-W:
hold on
2: to await something (as a telephone connection) desired or requested; broadly : wait
hang on
3 : hold on 2
Chambers
hold on! an exclamation requesting the other person to wait.
hang on colloq 1 to wait • I'll hang on for a bit.
CALD:
hold on (WAIT) phrasal verb INFORMAL
to wait for a short time:
Hold on, I'll check in my diary.
hang on (WAIT) phrasal verb INFORMAL
to wait for a short time:
(...)
Hang on a minute - I'll be with you in a moment!
DWDS:
umg. warte (mal) (einen Moment), das werden wir gleich haben
Dictionary: hang onto hang on | hung, hung | --- einen Augenblick warten