Is there a true contradiction between SN 5.10 and SN 22.85?

It is said by the bhikkhuni Vajira:

“Just as, with an assemblage of parts, The word ‘chariot’ is used, So, when the aggregates exist, There is the convention ‘a being.’ SN 5.10

However, in the Yamaka Sutta:

“What do you think, friend Yamaka, do you regard form, feeling, perception, volitional formations, and consciousness taken together as the Tathagata?”—“No, friend.” ... “But, friend, when the Tathagata is not apprehended by you as real and actual here in this very life ...” SN 22.85

Yamaka denies the aggregates taken together as the Tathagata is real and actual. On the other hand, Vajira seems to be affirming that the aggregates taken together is a convention. The words in pali for this phrase of real and actual are *saccato thetato* and for convention the word is *sammuti.* When he performed an analysis - as the Buddha advised Yamaka to do - he tried to find the *saccato thetato* self, but came up empty. Does that mean that Vajira erred in naming 'a being' as a convention? Is this a true contradiction? Why did the Buddha advise Yamaka to try and find a self through analysis? Wasn't this leading Yamaka into a thicket of views? UPDATE: This was too close to a seeded question. Although it was asked sincerely in that I was curious to know others responses (particular users on this site who I respect and admire) I do have my own idea of how I would answer this question (at least I do now and I'm not totally convinced I didn't have that idea already when I first opened it) so I should not have opened it out of mere curiosity. I was going to delete it given it goes against the site moderation guidelines, but then there are good answers and we are discouraged to delete questions where people have attempted to give good and thoughtful answers so I will leave it, but I do regret opening it in the first place.