Progressive rate springs provide additional support as load increases - load in the car and load on the suspension. To accept heavier load one logically needs stronger springs, but a heavy non-progressive spring would lead to harsh ride, already an issue in a Mini. A progressive spring provides a softer, more compliant ride when lightly loaded. This would tend to compromise handling except when you turn into a corner, weight shift adds load to the outside wheels, where the springs compress to a stiffer state. The inside wheels, being unloaded, get lighter springing which allows them to try to follow the unevenness of the road surface.
Progressive springs harken back to very early cars with leaf springs (think Model T). In a typical leaf spring each leaf is shorter than the one above it. With light load, the main leaf does most of the work but as load increases the other leaves take up the strain. It always puzzled me though that when a leaf spring broke it was not the main leaf but one or more of the subordinate ones.

Well it was a bundle of "I think and maybe's"  I'm trying to Law & Order this to lock down as much info as I can

thanks for the information on the spring and cones.  Are they all progressive rate springs?  Why does nobody use linear rate?

Those are aftermarket springs and adjustable cones for a Mini , they will fit any year Mini.
I presume you have no paperwork with the car?
A picture of under the hood and the inside dash area will help determine the year, failing that the glass is also date coded along with the trunk lock.

I'm helping my friend sort out her mini which is a basket of unknowns
Does anyone know what adjustable coil spring this is from her car?  Heritage believes the car the to be a 1987 based on the wiper motor - but no one really knows 

(let  me know if you can't see the above image, I'm trying to get use to this editor)

It looks very similar to most of the coil spring conversions I have found like this:
https://www.7ent.com/products/coil-spring-conversion-w-adjustable-struts-for017.html?VariantInventoryID=679&feed=Froogle&gclid=EAIaIQobChMIo6qZyL_A3gIVlKDsCh1gzAaXEAQYAyABEgKk3PD_BwE