Use Tools > Certificates, not Tools > Fill & Sign
Thanks @Bernd_Alheit. Very clear how I can control that.
It does solve my problem, but I am still not getting the rational behind these 2 features.
Just for understanding, why are there these 2 different methods and why sometimes, even the "Fill & Sign" menu brings a certificate signature into the document.
"Fill & Sign" doesn't use certificates.
May be that you have used a form with a signature field.