These are mainly technical differences. And the NWS makes these decisions, not TWC.
In Hermine’s case, there is no longer a closed circulation and the main convection (which produces thunderstorms and heavy rains) is well awaay from the center low.
But it’s still a nasty (non-tropical) storm that will produce some long lasting storm surges and depending on the wobble could hit some coastal areas with heavy rains and wind.
There is a very small chance of it regaining some tropical characteristics (circulation around a warm core) while it hovers over the Gulf Stream. It has a decent chance of becoming a sub-tropical cyclone however.
The NHC is still issuing advisories on Hermine even though it technically isn’t part of its jurisdiction anymore. This is fallout from Sandy when Sandy stopped being a tropical storm just before landfall and some idjits thought the threat was gone and didn’t prepare properly.
Forget what type of storm it is. That’s for the pros to think about. For regular folk, it’s about storm strength and consequences.
The Columbus Day Storm of 1962 is a classic example of a huge, incredibly, destructive, deadly storm that technically wasn’t a tropical storm on landfall. The East Coast press didn’t care since it wasn’t a hurricane and it hit the West Coast.
A cyclonic storm is powered by energy it receives from the sea surface. (Which is why they can’t exist in colder waters.) The water in the warm moist rising air in the middle part of the storm condenses and starts to sink right in the centre. The effect forms a positive feedback loop that builds ever stronger flows, and results in the extreme winds and the eye wall characteristic of a cyclone.
Once a cyclonic storm hits land, its power source is cut off, and the remaining storm is just a conventional low pressure system - a very intense one, and one that contains a heck of a lot of water - hence the massive rainfall. The critical difference is the loss of the downward flowing air in the centre. It stops because the source of warm moist air (the warm sea surface) to power it is lost.
Once it is on land it will continue to weaken and cannot rebuild. In principle a storm could change direction and go out to sea again - in which case it is possible to rebuild the counter-flow and become a cyclonic storm again. But this is pretty rare.
For an example of a rebuilt storm, check out hurricane Ivan on wiki. There was some dispute about the continuation of the path but it did become tropical again.
Several very-close-but-not-quite-right descriptions … so let me explain the basic difference between a tropical storm and an extratropical storm:
A tropical storm has at the surface a low pressure system, drawing moist air in. The air then rises up near the center, condensing water vapor into liquid water. At the top of the troposphere there is a high pressure system, and the air flows out away from the storm, literally an exhaust system.
An extratropical storm (a.k.a. a cold core storm) has a low pressure system from top to bottom. The rain-making process is through frontal action; warm less dense air is shoved up over cold more dense air for a warm front; or cold dense air slicing under warm less dense air again pushing air up for a cold front.
When meteorologists say a tropical storm is transitioning what is happening is that the high pressure system aloft is dissipating and becoming a low pressure system. Still a powerful cyclone, just it’s basic structure is different.
With Hurricane Sandy, this transition occurred before landfall. The NWS then dropped the Hurricane Warnings and replaced them with Hurricane Force Wind Warning, which is scientifically accurate. They got blamed for this because the average citizen thought 100 mph winds were perfectly safe as long as it wasn’t a hurricane producing them … meh … so now they continue to track the cyclone as though it was a hurricane, stupid people deserve the added emphasis.