The two bāʾ constructions share a particle but differ in what it governs.
Bāʾ with the source: It accompanies the original bearer, as “bihi” does in “la-tasʾalanna bihi al-baḥr,” where the pronoun refers to the man.
Bāʾ with the extract: A bāʾ of accompaniment appears with the imagined counterpart drawn out from the original.
Merely labeling a construction “bāʾ of tajrīd” is therefore incomplete. One must examine the governed word, the pronoun's antecedent, and the side on which rhetorical extraction occurs.