Aggregation, used strictly, means assembling many individual facilities under one owner so the combined portfolio is worth more than the sum of the pieces. The facilities may be bought one at a time, in small groups, or by buying the entity that owns them. The strict meaning is about the real estate ending up in one ownership structure.
The loose usage you're running into covers two other things. Buying a small operator including its people and brand is an operating-platform acquisition. You get real estate plus a management business, and you're paying for both. Rolling up third-party management contracts is a management-platform play, and vellum is right that you don't own the buildings there. You earn a fee, usually a percentage of revenue, for running someone else's facility. Those are genuinely different businesses with different risk. A management contract can be cancelled. A building can't walk away.
Price them differently. Real estate gets valued off NOI and a cap rate. A management book gets valued off the fee stream and how sticky the contracts are, which is much shakier.
The reason aggregation is talked about so much in storage is that the industry is unusually fragmented, with a large share of facilities owned by people with one or two of them. That fragmentation is what makes buying many small pieces a viable growth path. It also means most of what you'll look at was run by an owner-operator with no revenue management system, which is where the improvement case comes from and where the diligence work sits.