Cadets at my DD school are treated equally and provisioned equally. The only reason they know who is Scholarship and who isn't is that at her orientation just before school started, the scholarship cadets have a different paperwork packet to fill out, and for efficiency reasons, I suppose, each of those freshmen were given their paperwork packet as a group, separate from the non-scholarship freshmen present at orientation.
As to how it matters, as jcleppe pointed out, there are some training opportunities the summer after freshman (MSI) year that require that the participant be Contracted, which as an MSI means on scholarship. CULP is the one that is probably the most common that requires a contract to participate.
Otherwise, nobody cares who is scholarship and who isn't. Most cadets only pay attention to who is doing well in PT, and who isn't, since that is in front of everyone. Better to be non-contracted and doing well in PT, than contracted and doing poorly in PT.