I've forgotten/left my wallet at home

I want to say that I didn’t take smth. accidentally, unintentionally.
Ex: I left home, hailed a taxi and…I didn’t take my wallet, so now I can’t pay for the taxi.

can I say - I’ve forgotten my wallet at home or - I’ve left my wallet at home. Or both are correct? Is there any difference?

TIA, Jane.

I think “leave” should be used here not “forget". You can say, “I’ve forgotten to bring my wallet with me.”
leave (NOT TAKE) verb left, left
1 [T] to not take something or someone with you when you go, either intentionally or by accident:
Hey, you’ve left your keys on the table.

forget (NOT DO) / verb [I + to infinitive; T] forgetting, forgot, forgotten
to not remember to do something:
Don’t forget to lock the door.
Dad’s always forgetting (to take) his pill (Cambridge Advanced Learner’s Dictionary)

I’d think,

I left my wallet at home = I forgot my wallet at home >> ?I’ve forgotten my wallet at home >>…> #I’ve left my wallet at home

for the context.