Rewinding a motor or generator implies that the bulk of the damage that took the machine out of service occurred in either the stator or rotor winding - or both.
It can also be a decision based on planned outages - where the data trends indicate that the winding has not (yet) failed, but is losing its integrity. In this case - the decision is to install a new winding at a time that is convenient for the user, rather than when it will disrupt production.
Refurbishment implies one of two things. Either that the machine has nothing seriously wrong with it -just a little dust/dirt/debris that needs to be cleaned out, or there has been some moderate to severe mechanical damage that has not affected the windings but will reduce overall machine integrity (failure of a bearing or cooling system, for example).
In some cases it is true that it is more cost effective to simply replace the motor with a new one, but this is only for the smaller fractional horse power motors and depends on the mechanical condition of motor. Smaller single and three phase motors are extremely low cost on account of mass manufacture imports. It is a sad truth that a lot (not all) of these motors are substandard. Most do not even have phase insulation and an increasing number have no varnish at all. You can actually pull out the copper from stator slots with your hand! These issues are a major cause of failure. A lot of industry now buy many (containers) of these motors for backups for when the operational motors burn out. This reduces downtime for them, but in the long run still costs in frequency of downtime, the resultant effects and service costs. AS/NZS standards are very strict when it comes to the domestic/industrial wiring standards and for good reason, only when it comes to the quality of electric motors… nothing. Their eyes would pop out of their heads if they saw the standard of winding and insulation of these motors. I have even come across motors relying on the copper enamel as slot insulation where there was not even slot liner.
Winding is a very old trade and we have to work for our money. It is not "easy money" when you sell the client a new motor as quite often they can get a cheaper motor elsewhere and it takes time to pull down, check all mechanical and electrical aspects such as bearing housings and journals etc. Any profit made in mark-up is absorbed by this time to assess. There are larger international companies that will charge an enormous amount to simply look at your motor thereby negating this loss, however this stops many people getting motors repaired in favor of importing those "large containers".