Is "Filer's Federal ID No." the same as "Payer's Federal ID No."?

No, it does not mean the same, however it is used the same way as both are reported as the issuer of the tax reporting document.

Please refer to this link for additional information regarding the "filer's federal ID #":

Filer's federal ID #

The filer's federal ID # is used for the entity who files the tax reporting document with IRS and the taxpayer but who is not paying any money with the taxpayer.  For example, it could refer to a Form 1098-T filed for a student who received scholarship income and/or had college tuition and educational expenses with an educational institution.

The payer's federal ID # refers to the entity who pays the taxpayer and is reporting the payment made to the taxpayer and IRS.  For example, this could be someone who pays income to someone for working for them or for income received from them.  This could be referring to the entity issuing Form W-2, Form 1099-NEC, Form 1099-MISC, Form 1099-INT, Form 1099-DIV, etc.

[Edited 03/24/2021|4:00 pm pst]