Yes, semantics. This is a Team Model, which may or may not be a team ridden bike. It was a model sold to the public, and at least in the early 60's in the US was an upcharge over the Specialissima. It was also the only model in the early-mid 60's sold in the US in Celeste, the Specialissima's were only imported in other colors.

But basically it was the same frame as the Specialissima, but the Team model had no exposed chrome "socks" on the stays and fork, and had a decal instead of a head-badge. Which makes this one a little odd having the exposed chrome for the stays and fork. Which the seller confirmed was evident before the refinish, as well as there being no holes for a head-badge.

But as far as I'm concerned there's no "absolutes" for Bianchi, just good guesses. This may be a very first year Specialissima?

Anyway, the work was most likely done very well, and if you could put a clean correct parts group together for it would be a very nice bike.