These fuels are all related in that all of them are of similar boiling points and are distilled from petroleum from the same 'cut'. Gasoline is more broad in the 'cut' and has a wider range of materials in it. It also has additives that make it store less well. Coleman Fuel is a particular brand of the more generic product, white gas. White gas is gasoline without the additives in it yet, and may or maynot be a broad cut like regular gasoline.
They all have some very nice properties as a storage fuel. They also have some profound differences. Coleman fuel doesn't age and varnish up the way gasoline does. White gas is not as clean a cut as Coleman Fuel, but I've not done long duration storage tests on it. It might, or might not, store as well.
I've used several year old Coleman fuel with no problems at all. Gasoline more than 1 year old is marginal. Store it for a couple of years and it will smell of varnish and have odd deposits on the bottom of the can. All of these fuels are of a moderately high vapor pressure,so they can puff up cans in a hot trunk. Gasoline does this more, since it has more 'light' hydrocarbons. In some cold climates, these can even include Butane!
You will need a fuel bottle that can take some internal pressure if you intend to store gasoline or white gas fuels in a hot car trunk. I've done a multiyear test with Coleman Fuel in a Sigg fuel bottle in a Honda. It worked well. I've not tested Unleaded insimilar circumstances. If you do store gasoline, use summer gas. It has a higher boiling point and less light hydrocarbons. These fuels burn very cleanly. They are easy to light. They evaporate readily, so spills are to some extent self policing. The fuels are cheap, and readily available.
Unleaded gasoline is about the most commonly available fuel you could want. Stoves and lanterns to use them are available from many manufacturers just about everywhere. So why not just use gasolines or Coleman Fuel as your camping and preparedness fuel of choice? Why not, indeed. It would be a reasonable choice for most people. The stoves and lanterns do require pumping, which some folks find a bother. They must be refilled with a liquid, so you have a chance for leakage and spillage. Getting them lit when cold can takea while and does require a bit of a knack, especially for the lanterns. (You wait and wait and just about when fear has led you to believe that the lantern will blow up any minute, the gas finally reaches the mantle and lights, often with a startling POOF!)
For folks with no or little mechanical aptitude, Propane or Butane are better choices. If you have low availability of unleaded gasoline (such as someone living in a country where leaded gasoline still is the most common) or want a safer fuel in storage and don't mind the esthetics of use quite as much, then Kerosene is a good choice. For most folks, though, Unleaded or White Gas is the fuel of choice, and Coleman Fuel is just about the best brand. Once per year, about August, I cycle my stored gasoline. The old stuff gets dumped into the car (easy with a gas car, a bit trickier but still do able with a Diesel car). Then I buy a new fresh 5 gallons worth for the next year. The gas, being above the 2 gallon limit imposed by my home insurance for garage storage, goes into a detached shed away from the house. On a general use basis, I use Coleman Fuel. When fishing or camping, the clean burning of it, the lower smell, and the general convenience of a fuel that treats my appliances well is worth the added cost to me. In an emergency, I'd use my stored gasoline. There are an increasing number of stoves these days that can burn your choice of {unleaded, white gas, kerosene}, so the issue of which fuel to choose for storage is a bit less coupled to stove choice.
If you have a gasoline car, I'd opt for Unleaded Gasoline and a 'Dual Fuel' stove/lantern that uses unleaded and improve the storage system by putting the fuel in an insulated container like an ice chest (sans ice). The goal is to cut the peak temperature experienced by the stored fuel. The insulation of the ice chest would help do this. Coleman fuel is my emergency stove and lantern storage fuel of choice for all things other than my present car, where I use Kerosene, since I can run my Diesel on that in a pinch. For the average person driving a gasoline car, I'd use Unleaded gasoline in a Sigg or MSR type fuel bottle and appliances made for white gas/ColemanFuel/Unleaded.