Question about appeal to force fallacy

1. Does an argument contain an appeal to force fallacy if it is about accepting/rejecting an action rather than imposing a belief. For example if the argument goes along the line of  'if you do not do action x, you will suffer punishment y. Therefore you should not do action X'

2. What is the difference between a threat and an argument?

In case 1) this is the non-fallacious use in my opinion. This is because rather than threatening someone with physical punishment, for example, for accepting/not accepting a belief, it is a warning of the consequences of not taking an action. It is still  ad baculum , but not deceptive.

Non-fallacious form (substitute x for, say, 'go to bed on time', and y for 'losing your smartphone privileges')

• if you do not do x, you will suffer y
• you do not want to suffer y
• ergo, you should do x

The fallacious form would require forcing you to accept a belief (substitute x for, say, 'Jesus Christ is Lord', and y for 'death').

• if you do not believe x, you will suffer y
• you do not want to suffer y
• therefore you must accept x as true

2) An argument is a series of statements intended to defend a proposition, or point. A threat is simply a warning of the use of force or other undesirable consequences (coercion). A valid argument proves its point without relying on force. If I am forced to accept, for example, Jesus Christ is Lord on pain of death, it does not  prove  that he is in fact, Lord. All it does is prove that I was coerced. 

Hope that helped.

 'if you do not do action x, you will suffer punishment y. Therefore you should not do action X'

I had to restate the the central idea of the question to answer it. 

'if you do not do action x, you will suffer punishment y. Therefore you should do action X'

...though this works as well

 'if you do action x, you will suffer punishment y. Therefore you should not do action X'

Either reframing makes it appear as a lawmaker's output, and is not a topic for fallacies' analysis on its surface.

Laws on speeding, parking, seatbelt wearing, spitting on the subway, nudity at the beach all might be discussed to find out what rational basis underlies the law, but by the time it becomes eg USC 2590:1a-3c, rationality is not part of the confrontation between an officer and a respondent.

The basis for laws is presumably that it makes sense to a sufficiency of the populace, but for those who do not agree with the basis, it is simply coercive, not an appeal to force, though it may in general expect an overall to appeal to authority.

So imo, it's first an appeal to popularity (everyone else does it), then authority (the lawmaker says to do it), but in the final analysis is a threat.

Much of the time, one must enjoy the hospitality of the state before gaining the privilege to contest laws. Governments do not tolerate arguments, unless/until they perceive credible threats.