Remake? Adaptation? Remix? Homage?

I had the pleasure of attending a fiftieth anniversary screening of Fellini's film 81/2 earlier this month. It was a little odd, because I had already seen the musical Nine, which in retrospect was the wrong, wrong way round. Also, Nine is not very good.

The thing that really struck me was how the sequence with La Saraghina from 81/2 gets reworked in Nine. The Fellini sequence goes something like this (for the full contrast of Fellini after Rob Marshall, you might like to try watching the second clip first):

The sequence in Nine, starring Fergie in the role of la Saraghina, goes like this:

The director of Nine is Rob Marshall, who previously made Chicago, so the big lush musical numbers are a gimme. But is it just me, or does this sequence also borrow shamelessly from the staging of 'Mein Herr' from Cabaret and the production values from the 'Tango de Roxanne' in Moulin Rouge?

So what is this? Remake, homage, remix, adaptation, pastiche? I'm stumped. Answers in the comments please!