The Gillette Slim was "the improved FatBoy" and the first batch was produced in 1960-Q2. There were no more produced until 1961-Q3 (G3) and it ran until to 1968-Q4 (N4).
Like its predecessor, it's also a 1-Piece TTO razor with 9 settings, numbered 1 to 9. Visually, the doors have a lower and less rounded profile than the FatBoy. The handle has the same knurling as the Executive (Gold) FatBoy however is longer and thinner. The also changed the profile and knurling of the adjuster dial.

It was marketed as the "Slim" in the USA and Australia but the UK it was called The Adjustable Mk2. In the USA it initially sold for $1,50 and that was later increased to $1,79. The handle length is 81mm and the complete razor weighs 71 grams.

There were two minor design changes through the 7 years (see images below) and it was Gillette's adjustable Razor at the time when the now very sought after "Spoiler" blades were introduced.

The patent was granted on 05 October 1965 and the patent number is US3209454 (Click to see).

How do they shave?
I find them slightly better shavers than the FatBoy.

Slim Design Changes
There are two very small design changes that have been noticed by collectors.
The first (left image) - the design of the bottom edge of the positioning bar/door actuator was changed between 1962-Q3(H3) and 1962-Q4 (H4).
The second (right image) - the design of the hinge tab of the doors between the 1964-Q1 (J1) and 1962-Q2 (J2).

Delta Echo and North Shore Slims
I have two Slims that have been coated.
The first is my birth razor which was done by North Shore Razors. The coating is Guncote and it was done by them in May 2017.
The second is a Cubano Edition by the now defunct Delta Echo. Delta Echo used Cerakote and the Cubano Edition was one of their "Standard offerings".