define your terms! "Pilgrim's passport" is sometimes used as an English term for the credencial, although 'credentials' would be the straight translation. The CSJ calls their version "Pilgrim Record" specifically to distinguish it from the credencial. As marktqm says, this is a distant descendant of the credentials (= letter of introduction) carried by a medieval pilgrim as identity papers. Of course, today's credencial, whatever you call it, isn't really 'credentials' as it has no authority behind it. Incidentally, one of the first things the Société des Amis de St Jacques did when they were founded in 1950 was to issue a letter of credentials to prospective pilgrims.
Originally a passport was a permit, literally to pass through the port or entry point to a city or territory. So today's national passport, as identity papers, is descended more from the credentials than from the passport which is more like a visa.
Hope that's clear!