From my experience, a smoke test is like testing a new toy to see if it even turns on. It’s that first check to ensure the major functionalities are working as they should, with nothing critically broken. Now, a sanity test is more focused — it’s like checking a specific part of that toy (say the sound button) to ensure it works after a fix.
In short:
Smoke test = ‘Does everything work at a basic level?’
Sanity test = 'Does this small fix work as expected?