A general contractor may hire any kind of sub-contractor. This includes but not limited to lifting contractors, who may in turn hire cranes, riggers, scaffolding, operators and technicians, etc..
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Any contactor can be used for either purpose, but the current ratings are lower when used in 'inching and plugging' mode as they are in cranes and hoists.
For any general motor starting duties, select your contactor on the basis of the AC3 rating.
For inching and plugging, select the contactor on the basis of the AC4 rating. Your contactor supplier will be able to supply this information.