There are lots of forms that can basically do what you want. Why do you want them to fill in a PDF form? That’s harder to find. But filling out forms, and then having a PDF record of it plus saved to a databse, is quite possible
There may be other options for you, but I use MachForm. Saves to database, all entries can be downloaded as PDFs, and has a ton of other features. More here: https://www.machform.com