peregrinus

Peregrinus, peregrini, m., second declension, from the adverb peregre, "abroad", which is per plus ager: one who is out through the fields, beyond the boundary.

In Roman law the word is technical. A peregrinus was a free man who was not a Roman citizen, tried under a separate praetor and a separate body of law, the ius gentium, so it marks legal status rather than distance travelled. Christian Latin then turned the outsider into the traveller to a shrine, and that sense reached English as pilgrim through Old French pelerin, the r becoming l on the way, which is why the English word looks unrelated. The word also works as a plain adjective, "foreign".