Neither of the scenario that you mentioned is true for me. I was working on F1 after I graduated and I left the country after I used up my STEM OPT (1 yr) + Extension (additional 2 yrs) and moved to Canada. In b/w I applied for H1B but it was not selected in the lottery so I've no option but to leave the country when my F1 status ends since I'm out of status now. So I was in F1 status (working) till October 2019 and then moved to Canada For November and December 2019 since I'm out of status to stay in US.
Let me know if you need any additional details.
