Arminians use the term freewill to describe their view of men’s decisions. I note that some Calvinists also claim that man has freewill. Their view they call compatibilism which I admit struggling to grasp. It seems to me that compatibilism is determinism with the claim that the person is also choosing this path.
Arminians think that people can make free choices that are contrary to God’s desires. That is men have the power of contrary choice. God can say that a man should do A and that he desires A, and that his purposes would best be fulfilled by doing A, and yet a person can still choose not to do A.*
To distinguish such freedom oftentimes the term libertarian freewill is used. I take this to mean that a person can make a choice of their own accord. While a man may have several influences on his decision, such a choice is ultimately at the level of the person—his will, his decision making centre. The libertarian adjective is to identify that the decision is sourced in man, as opposed to a compatibilist claim that the man’s decision is sourced in God. It does not mean that a man can make any decision whatsoever! Clearly it does not mean that a person can choose to fly. But nor does it necessarily mean that he make any choice that another person is potentially capable of. He cannot make decisions based on knowledge he does not have. If unredeemed man is unable to make decisions to follow God, he still can make a variety of decisions in rejecting him. And he can refrain from making some bad decisions.
This falls under item #4 of my top 10 Calvinist annoyances. The extremes are that freewill is either essentially God’s decision (compatibilist†) or man has the full capacity to make all and any good or bad decision.
The middle position is that man has the power of contrary choice, though his decisions will be limited in capacity by various things.
*Note that this does not mean that God is unable to force the person to do A. But in doing so God has removed their freewill.
†I am not intending to misconstrue compatibilism. It is a Calvinist term and I am happy that they define it. Feel free to correct me.