I personally don’t limit consooming to just objects. I consider it to be the whole “consume product, get excited for next product” mentality, where the focus is more on obsessively acquiring or experiencing whatever the latest thing is, and either ignoring or mentally discarding older stuff. I think the concept can apply to anything from objects to TV shows to video games, as long as the emphasis is more on participating in the hype-saturated culture than on actually enjoying the content/object itself.
I tend to think of collectors more as people who can also be obsessive, but tend enjoy the object of their hobby for its own sake. Collectors also aren't afraid to specialize or limit themselves to a particular niche, and often prefer to in the interest of preserving their budget, time, and space.
So for the example of stamps, I'd consider you stamp consoomer if all you did was just grab every single new design the USPS produces, and that was your only goal. I presume most stamp collectors, though, tend to focus on seeking out stamps from particular countries, time periods, artwork, etc.