the rate law is an expression (can be also called rate law expression).
it would be something like:
rate law = [A]^a^b
rate order would be the exponents in the rate law.
so total rate order of the above rate law = a+b
order in respect to [A] = a
order in respect to = b
the rate law can, and should, be determined by data where you have actual values derived from experimentation.
it can also be determined through mechanisms focusing on the RDS (rate determining step) but the rate law determined by a mechanism must agree with the rate law determined by experiment.