In matchplay you are tasked with protecting your own interests under the rules (Rule 3.2), this simply isn’t possible in strokeplay when it is the interests of “the field” as a whole which need to be protected – and the whole field can’t play together in one group (which is a requirement in matchplay).
As an example, think of the scenario where your opponent plays from the wrong teeing area – in strokeplay it’s a 2 stroke penalty and the mistake must be corrected (Rule 6.1b(2) – in matchplay you get to decide whether to count or cancel your opponent’s stroke, depending on where it has finished (Rule 6.1b(1). SO if they have put it into a penalty area or deep in the trees you might let the stroke stand because you feel it would be to your advantage – however if they have hit 350 yards and split the fairway you might ask them to play again. (NB If you are aware before they play that they are in the wrong place you should stop them before they play – otherwise a great way to lose friends!)
The order of play is also fundamental in matchplay so ready golf is not an option – a player may cancel an opponent’s stroke made out of turn (Rule 6.4a(2)) – although you can agree to play out of turn (Exception to Rule 6.4(2)), if, for example, a player nearer the hole can only play sideways due to their position.
Finally, this responsibility to look after your own interests does not extend to agreeing between you to ignore any Rule (including a local rule) or penalty that you know applies. If you do this then both players will be disqualified (Rule 1.3b(1)) as soon as one of the players starts the round – even if the agreement has not yet been acted upon.
The following posts will take you through a few matchplay scenarios.