Is there a difference between a 'pure number' and dimensionless quantity

Question

I see dimensionless quantities described as 'pure numbers' I mostly understand this in terms of ratios (angles, a lot of dimensionless constants) as we are not really counting or measuring anything but what about something such as the number of coils in a Solenoid. We treat this as dimensionless even though we are counting something, even in the sense of ratios or dimensionless constants, though there is no dimension in the sense of Length, time etc but they are still quantities of a system and quantify something about it, so they aren't pure in the completely abstract way that mathematicians use them.