I've had a quick search for "colour chart" but can't find it
Birch and Claredon grey
Are both more more or less grey. Rose taupe is also grey, So is smoke grey
There are probably more variations of this grey theme.
It looks like a decent paint job from here and you should be able to get a good match from a paint place for touch ups.
The question is, do you want originality (greyish) or are you happy with what you have?
I'm actually resisting having my car ( Rafferty ) resprayed as I feel its character would be reduced by losing some of the shades of green its been painted with over the years its been around for 40 and I'm quite proud of that.
Its not up to 40 shades yet but well on the way.
I spent a few hours with an electric buffing machine trying to raise a shine on some very sorry old paint to this end recently.