[Random House Dictionary], s.v. make
3. to cause to be or become; render: to make someone happy.
8. to cause, induce, or compel: to make a horse jump a barrier.
What’s the difference between 3 and 8 in their meaning?
Both uses of make have the sense of causing something to be predicated of the Direct Object. There are a couple ways of parsing this, and it doesn't really matter how you represent it
[Subj] MAKE [non-finite clause [Subj2] [Pred] ] ... OR
[Subj] MAKE [arg1 [DirObj] ] [arg2 [Pred] ]
The difference between 3 and 8 is that in 3 the verb in [Pred] is omitted, because it is a copula (BE, BECOME or the like) and its 'sense' is already evident in MAKE, while in 8 the verb must be included because it is an action performed by [Subj2].
- I made the horse happy = I made the horse [become] happy.
- I made the horse jump the fence.
There are other constructions besides MAKE which have the same sense but call for different arguments. Where MAKE takes the unmarked infinitive in [Pred], CAUSE takes the marked infinitive and does not omit a copular verb in [Pred]. More elaborately, BRING IT ABOUT requires a finite that clause.
I caused the horse to become happy.
I caused the horse to jump the fence.
I brought it about that the horse became happy.
I brought it about that the horse jumped the fence.
The basic difference is that the verb cause in English cannot be followed by an adjective, only a verb or a noun.
The following mean the same thing:
I made him happy,
I caused him to become happy,
*I caused him happy,
is wrong. So if make is followed by an adjective, the definition must be to cause to become or to cause to be.
On the other hand, you can say both
I made the horse jump the fence,
I caused the horse to jump the fence,
so if make is followed by a verb, to cause to is a good definition.
The major semantic difference is that meaning #3:
to cause to be or become; render: to make someone happy.
means that you or another living being or Mother Nature has done something that induces a feeling a joy, pleasure, or happiness in someone. The someone who is happy because you, e.g., smiled at him, his dog was excited to see him, or it snowed and school was called off for the day. When I was in the Navy, our base commander tried to "make us" feel a positive emotion when he told us that everyone would attend the Christmas party, and "you will all have fun!" Impossible! He could make us all attend the party by threatening to punish us if we didn't show up, but he certainly could not make us have fun and enjoy ourselves.
Meaning #8, however:
to cause, induce, or compel: to make a horse jump a barrier.
means that you or another living being or Mother Nature has done something that forces someone else to do something, probably against her will, e.g., you've pointed a gun at her and demanded that she give you all the money in the cash register, a bee sting made her wince in pain, or an earthquake made her flee for her life. Horses don't go jumping fences for the hell of it. They jump on command (meaning #8) or when they want to escape a corral.