रेलफैनों की तो बात ही कुछ और है

The term 'Push-Pull' is used to refer to trains comprising unpowered train sets with a propulsive unit (which may be a locomotive or multiple unit) at one end only. The unpowered units have multiple unit control equipment so that they can control the propulsive unit which pushes them in one direction of travel and pulls them in the other.
Most EMUs are, to some extent, push-pull, because often the motored vehicle is in the middle of the unit, not at the ends. Thus in any EMU train, some cars are being pulled and some pushed.
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advantage of this is that the engine or propulsive unit does not need to be removed from the train at termini because the train can be driven from each end. It is an intermediate step between normal locomotive-hauled operation and full multiple-unit operation and which can be used where full electrification of a route is not economic. It can also be used where hauled stock is not life expired and the provision of suitably equipped driving trailers allows it to be used instead of being replaced by new multiple units.
Source : www.railway-technical.com/pu-pl.shtml

Not May Be, It is
I have given you the source of info
Also your definition is right for the trains which is having engine in middle.
Check my posting @ Today (07:18PM)
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of information is also given again.
Thanks & Regards