A cloud model can be large because the constraint is cost per query. An edge model has to fit in the memory that is physically present, complete within a cycle time set by a machine that will not slow down, and do it on the power a battery or a passive enclosure can supply.
Those constraints interact. Reducing precision saves memory bandwidth and energy, but shifts accuracy. Pruning reduces computation, but irregular sparsity often runs slower on real hardware than the dense version it replaced. A smaller architecture may be worse than a quantised larger one. None of this is settled by reading a paper; it is settled by measuring on the target.