I think the key is in the word "different," which can be used in at least two ways. "Her approach to the problem was quite different." AND "Different strokes for different folks." Why can't you say, "Different stroke for different folk,"? You could say "I decided to try a different stroke," but it's definitely countable. It's this second usage of "different" that makes it countable. You could not say, "I decided to try some different stroke." It would have to be plural. "I decided to try some different strokes."
You could say, "I decided to try some different paint, or some different makeup. This would be uncountable. If we say "I decided to try some different paints," (I'm an artist) I mean different from the ones I was using before, not different from each other.
In your "example to compare," you use "some/a lot of" which are used to describe both/either countables or uncountables. Different, in the original sentence, is only used for countables.
I admit it does seem complicated, and my explanation is not as clear as I'd like it to be. "Strokes" is a bad example, because it's only countable.
- A.