Under property institutions, private or public, a person who wishes to use property that is not his own must induce the individual or group controlling that property to let him do so; he must persuade that individual or gorup that its ends will be served by letting him use the property for his ends. (my emphasis)This quote illustrates a primary way libertarians conceive of 'persuasion'. It means, roughly, to get someone to do something voluntarily. Many people think the word 'persuasion' has hidden undertones of controlling people; it's not meant to.
Friedman explains the three ways you can get the use of someone's property: love, trade, and force.
He means love broadly to include anything where you want to give me something for nothing because you love, value, appreciate, or approve of the goals I'm working towards, or otherwise want to see the resource used in the way I will use it.
Trade includes any scenario where I give something in return for the property.
And force, like love, is something for nothing, but in this case it's not voluntary.
Logically these three categories cover all cases, but it's awkward where to put getting something via psychological manipulation because it's not obvious whether it counts as voluntary or not. So perhaps we should add a fourth category for it.
With that category in place, then persuasion means love or trade, but not force or manipulation. You can persuade someone to give you a car by trading him some money, or by explaining that you're going to use it to do something he approves of, such as use it in a well publicized race (so he'll enjoy having his car featured in the race). But if you use force or manipulation that is not something we would refer to as persuasion.