Micro Inverters, Power Optimizers, Power Controllers and Power Regulators.

During solar power harvesting process the electrical power obtained from the solar panels and juiced down in large amount to banks of energy storage (batteries) or used on conventional loads has to be voltage and frequency mitigated  in order to obtain maximum efficiency. The process of mitigating the PV electrical power it is done using power optimizers, power conditioners, power controllers and power regulators.

Is there a difference between a micro inverter and a power optimizer and what is that difference?

A micro inverter is mounted under a solar panel (or solar module) performing the role of a string or array inverter at panel or string level. A micro inverter receives DC current respective DC voltage from that panel or string of panels and convert respective transfers the received power  along the home runs as alternative power straight from underneath that panel where it is mounted and takes care to harvest the power at the max power possible value through MPPT optimization performed at panel or string level.

A power optimizer is a DC to DC power conditioner based on a strict path which follows the I - V curve for that specific module or string of modules. In this way it will  achieve maximum power generation from that panel during sub-optimal module operating conditions caused by shade or soiling and being able to recover over 50% of system power loss. A power optimizer works complementary to a string or array inverter increasing site MPPT performances and allowing a full  fledge inverter mounted on the DC site downstream from the power optimizers to improve protection respective to add load management and grid connectivity functions. 

What is the common benefit using either a power optimizer or a micro inverter?  

They do have things in common. They are both mounted individual under a module and they do leverage the control at module level and they both eliminate the Christmas Tree Effect allowing modules to be parallel connected and in this way when one it is invalidated the rest of them are working full steam offering the best efficiency for the PV plant.