In my mind, there's actually a very simple delineation between the two of them.
The first - a statement of Consequences - doesn't tell you that you "can't" do something. It simply informs you of what you can expect to see happen in response to Your Chosen Actions.
Example of a Statement of Consequences:
It's up to you whether you pay your bills..... or instead decide to go out to the movies, go camping for a couple of weekends out at the area lake, and take a trip out of state over the course of a weekend as a sort of mini-vacation.
The consequences of the first: your life doesn't really change. Your electricity, gas, water, and cable all stay connected, your car is not repossessed, and you are left alone by "the powers that be" (the folks where you had bills due.)
The consequences of the second: Immediate gratification on a superficial level, followed by all kinds of Bad Things happening to you. You have a lot of fun out camping, and spend some great time with those folks you went to see while you were outta town. However, when you get Back, you find that you no longer have Electricity - which means nothing works in your house, you get to go hungry, all the food spoils in your fridge that no longer works, you can no longer relax after work watching tv or playing that favorite video game - and your car has been repossessed. Which, of course, means that all your Other bills are going to be past due and get cut off in the near future, because you now have no means to get to and from work. Or to and from those fun camping trips, the visits with outta state friends, or the grocery store for milk (which, hey, ya can't store anyway - cause ya chose to spend your money playing rather than being responsible!)
Example of a Threat:
If you don't pay this bill, I'ma send a couple big guys named Guido 'round to have a lil "Talk" wich ya - and they're gonna start breakin bones til it reaches an amount equal to whatcha owes me, see?
Not easily confused, but some people manage to do so anyway...
Here's hoping that none of my readers mistake the two, or ever do anything to cause the second to come to pass...