Both structures can mean "to persuade or order someone to do something," don't they?
Possibly, yes, but that isn't normally how the former is used. Why have you mentioned
make somebody do something? That's a different pattern. Let's not complicate things.
I'll explain it my way:
1)
have somebody do something
Form: have +
object +
bare infinitive phrase
Meaning: The blue part is a verb phrase, signifying an
action. The verb
have is causative, the red part is the object (almost always a person/people) upon which the causation is effected, and the blue part is the action that is caused.
Use: This pattern is typically used to talk about ordering people to do things. It is usually the case that there is one party who has some kind of authority over another.
2)
have somebody/something doing something
Form: have +
object +
adjectival phrase
Meaning: This is also causative, but has the sense that what is effected (the blue part) is a
state-of-affairs rather than a single action. In other words, there's a sense of progressiveness that doesn't exist in the former pattern, thus the -
ing form.
Use: Unlike the former, this pattern is not most commonly used to talk about giving people orders. Notice also that the 'state-of-affairs' that is caused need not be expressed as a verb phrase. I'd say it's just as likely to be expressed with a preposition phrase, as with the first two of the following examples:
He had me in stitches.
Her beauty had me on my knees.
Bob's back pain had him writhing in agony.
