And you can fill in a form because you're supplying missing information. Fill out is generally used when you tell someone to enter all the fields on a form of more than one field. Example: Please fill out this form. Fill out means to complete by supplying requested information.
Assuming you are an Italian currently in Rome At the beginning you fill out I Giorgio Aptsiauri, country Italy, date of birth 1 Jan 1990 At the end Done at Rome on October 26 2020 As @KateBunting suggested in a comment forms in the UK do not usually ask you to say where you filled it out but in some countries this is more common.
In my experience (Aus) a prescription is filled out (sometimes abbreviated to filled) by a pharmacist when the medicine is dispensed. Forms are sometimes filled out, but more often filled in.
If someone asks you to fill them in, meaning to brief or inform them about something, could it in any way be construed as an invitation for sex, as when a girl playfully says so in response to, "I ...
NBC Chicago: How to Fill Out Form for Illinois Income and Property Tax Rebates as Deadline Approaches
How to Fill Out Form for Illinois Income and Property Tax Rebates as Deadline Approaches
The form for those 65 and older is easier to read and fill out Reviewed by Lea D. Uradu Fact checked by Suzanne Kvilhaug To simplify taxes for those ages 65 and older, the Internal Revenue Service ...
NBC Chicago: Deadline Just Days Away to Fill Out Form for Illinois Income and Property Tax Rebates