Why do these two Gremlin queries return different results when adding a project but otherwise keeping the count query the same?

Question

I'm using Gremlin, and I've got these two queries that return different results and I can't understand why.

gremlin> g.V().
    hasLabel('person').
        has('person','personId', 'd6688539-7773-4126-93bf-bb8ef979e25a').
        bothE('is').
        otherV().
        hasLabel('face').
        bothE('is similar').
        not(inV().bothE('is')).
        otherV().dedup().
        count()
==>3

gremlin> g.V().
    hasLabel('person').
        has('person','personId', 'd6688539-7773-4126-93bf-bb8ef979e25a').
        as('person').
        project('personId','name','count').
        by('personId').
        by('name').
        by(
            bothE('is').
            otherV().
            hasLabel('face').
            bothE('is similar').
            not(inV().bothE('is')).
            otherV().dedup().
            count()
        )
==>{personId=d6688539-7773-4126-93bf-bb8ef979e25a, name=Shawn, count=1}

Why do they return different results? And what do I need to do to the bottom query to get it to correctly return 3?