When referring to a form, In the US they are both used interchangeably, whereas in the UK we tend to say "fill in". "Could you please fill in this form whilst you wait?" "Due to COVID regulations, you're required to fill out this form" Either of these would be ok. You can get around this by saying "Please complete the form below" However when referring to a single field in a form, "fill in" would be better "Please fill in your name in the box below"

accidentally wrote a comment instead on an answer - see answer.

Fill out is mainly used when talking about completing something with information, like a form or a survey. e.g. "Please fill out this form!" = complete the form. Fill in can mean: 1. act as a substitute for someone when they are unable to do their job. "I'm filling in for Jane today." 2. to give someone details about something "She filled me in about what happened." 3. fill in a form like your address, name, etc. 4. the physical action of filling something in like e.g. a hole on the wall.