Difference between Möchten Sie and Haben Sie Lust

Is there a difference between when to use mögten versus haben for purposes of expressing "would you like?"

Within the material examples it's difficult to determine if there's really a difference. For instance there are a couple of examples like the following:

Möchten Sie noch etwas? with translation "Would you like anything else?".

Habt ihr Lust ins Kino zu gehen? with translation "Would you like to go to the movies?"

Are these interchangeable or is there a subtle nuance on when to use one over the other?

Our tutor is usually very slow to answer queries so I will have a go.
I asked a native speaker about it they said that möchtest du and hast du lust are very similar and can often be used interchangeably but there is a subtle difference.
Probably rather like the difference in English between:
I would like.../would you like
and
I feel like.../do you feel like

These can be used interchangeably but there is a subtle difference. I find it hard to describe a definite rule but hast du lust seems to be a direct translation of do you feel like..

​As a native English speaker you can probably think up situations where you would prefer on or the other.

There is a German with Jenny on hast du lust here: 
https://www.youtube.com/watch?v=fyX3qGopfFI

 

Thanks for the info - that makes sense to me. Hast du Lust has a literal translation of "do you have desire" so I can see that being more toward "do you feel like" as opposed to "would you like". I think the difference makes sense to me now. Thanks for the link to German with Jenny - she looks like a terrific resource!

Yes, German with Jenny is one of my favourite German channels. She covers a lot of stuff that appears in Rocket German but isn't explained.