When do I have to use rectifier-inverter, and when is "dimmer circuit" sufficient in driving AC motor?
A Triac 'dimmer circuit' chops the front end off each half cycle and so lowers the effective voltage to the induction motor, causing it to slip more and run at a lower speed. The main disadvantage of this method is high harmonic content, which causes excess heating in the motor.  

If mechanical loading is strongly dependent on speed (eg. ceiling fan, water pump) then the load is also dramatically reduced at low speed so motor heating may not be a problem. If high loading is expected at low speed then a VFD is more appropriate.

There is a third option which is better than a Triac dimmer but simpler than VFD -  Single Phase PWM. This still works by lowering the effective voltage and causing slip, but eliminates the higher harmonics that cause excessive heating. Here's an application note that explains the technique:-

PWM Control of Single-Phase A.C. Induction Motor Using MC68HC908