In the Wikidata Item View UI are several widgets to add data.
Some indicate what they will add (reference, qualifier), while some don't (statement). We should be clear on that in all possible cases.
Suggestion: Introduce "Add statement"/"Add property"
Open question: It is possible to add a completely new property/statement or to add a statement to an existing property.
I assume we could call them "add property" (all new) and "add statement" (if we add an additional statement to an existing property on the item, e.g. yet another club a football player played for) – but I might mess up existing terminology here.
General Principles: »I want to know what an interaction causes« (principle of least surprise) and »stick to standards«