Question on visa check requirements

Hello,

I am a non-eu citizen that is going to fly from italy (venice treviso) to spain. I hold a D type multiple entry visa and an expired permit of stay with a document stating I am on the process of renewing it. The information regarding whether with these documents I can travel to other schengen countries or not, is complicated and not uniform. I am sure (by experience) that different attendants at different airports would behave differently, so I am not sure what might happen.

Previously with Ryanair if you were flying in between Schengen countries it was only an `identity check` at most. Now that they call this a visa check I am curious whether if they really check visa or do they just check the identity of the person.

Thanks