Hi CyrilleB,
I'm no expert, but I guess the nuance is that when you write Δ you are saying , "this is a I or IV chord" (if you see CΔ you are kind of free to play C, CΔ7, CΔ9, C6, etc.) and when you write Δ7, what you're saying is "This is a I or IV chord and you have to play the Seventh".
But...