Do the two terms mean the same? mass production rate, mass flow rate and mass consumption rate in a solid propellant rockets.
Agreed that it's hard to give a definitive answer without the context in which they are used. But taking their definitions literally based on the terminology:
mass production rate = rate at which product gas mass is generated by burning propellant (no mass can actually be "produced" here, but if we are looking at a nozzle, the mass of interest is product gases, which are being "produced" by burning propellant
mass consumption rate = rate at which propellant mass is converted to product gases (aka the rate at which propellant is combusted)
mass flow rate = the rate at which mass is flowing through the nozzle
Based on these definitions, the first two are equal if the only mass being ejected from the rocket comes from propellants. (I am intentionally neglecting mass changes due to staging, since this question is likely in the context of engines/nozzles). This is a reasonable assumption, since if you are changing the mass of a rocket from anywhere besides the propellant/fuel/oxidizer, that means something is very wrong (melting engine, breaking hardware, etc.)
These two terms should be equal to the mass flow rate when the motor is in steady state operation. If we consider the control volume to be the entire rocket nozzle/combustion chamber at the surface of the solid propellant (so that unburned propellant is not in the control volume), then based on conservation of mass, any "produced" or "consumed" mass is the mass entering our control volume. This mass can do two things: exit the nozzle by flowing through it (mass flow rate) or stay inside some portion of the nozzle.
The term steady-state indicates that the flow at any point in the nozzle is not time-varying, which means that a unit of mass that enters our control volume must exit it (mass in = mass out). Otherwise you would have a changing amount of mass at some point in the control volume, which would show up as the density at some point changing as a function of time (not steady state). So in steady state operation, all three terms would be equal.
The non steady-state case is generally during startup or shutdown (also during any times when mass flow in changes and the system is still responding). The mass flow through the nozzle is driven by the chamber pressure of the motor. When the mass flow in (controlled by the rate of propellant combustion) changes, the system must reach a new equilibrium chamber pressure that leads to the mass flow rate through the nozzle equaling the mass flow rate in. This is not an instantaneous event, since a sudden increase in mass flow in would cause the current chamber pressure to be too low to push all the mass out, which would lead to a buildup of mass and an increase in chamber pressure until the in and out flow rates are equal.