From what I understand, the 'rat' term was used to describe motorbikes and cars that are kept going with no recourse to new parts or proper maintenace schedules. If it breaks then fix it with what ever comes to hand with minimal cost and effort.
It lead to vehicles that are kept working with anything, hence the piles of scrap parts, and were never cleaned or properly painted over, hence the rust patches.
Modern rat fashion is the complete opposite.
Effort and expense is put in to paint removal in the same way as stone washing and prefading new jeans.
Items of scrap are bought and then fixed on to look 'just so'.
My hack bike is a true rat. I got it on freecycle, it has the wheels and pedals from a scrap yard find, the seat came off a bent and twisted sub £100 MTB, the cables were made up form shortened cables left over from my KMX, the brakes were made up from bits I found in a box of assorted bike parts that came with a Silver Fox frame, the chain is the best bits of scrap chain linked back together to make one long chain.
The only 'new' parts are the MTB tyres that came off my Marin when I put road tyres on it.
My car is also a rat in the making. It still looks great as a car but slowly the gaffer tape and zip tie repairs are showing in the wheel arches, the blobs of paint on the bonnet are just to stop holes from appearing from stone chips, The additional wiring to make things works are stopping the carpets from lying flat.
It has a towing pintle and a winch, a bit of PVC gutter over the back seat back to allow long lumps of wood to be slid in onto the dash board, wires poking out from the dash to run the satnav, phone and FM transmitter. I fixed one of them last night with a band aid.
It will gradually decay away in a pile of gaffer tape and zip ties a I run it into the ground.