I think the only reason people say it's a Miata is b/c they are the most well known "small convertible" around...and they're everywhere. I see at least 4 a day. I doubt most non-car people even know that they're both rear wheel drive. Honestly, they look NOTHING alike to a car person, but if you didn't know any better, I guess it could get confusing.
Here's an old pic of my car with a random Miata:


I have nothing against the Miata at all, I've been on a few cruises with them back in the day, my father in law has a sweet one and he used to belong to a club.
It doesn't bother me if someone calls it a Miata, I just tell them, "nope, it's a Honda " and be done with it.

 

I'm not sure why but when I see a miata I think it's "dinky". Yet I drive an S which isn't much bigger but it seems like the S is small without looking "dinky".

 

The brakes on the NC is phenomenal. I had a leased NC for 2 years before I got the S. I test drove a S and while backing out of a driveway I almost hit the car parked behind me and I also missed a stop sign by about 3-5 feet.

 

I would like to see someone clear a turn without turning the wheel.

If only Initial D physics was real. Lol

 

Better shot of current MX-5 showing some S2000 styling cues:

 

I hate the toilet bowl lid hood of the NC...lol

 

No your right actually, never tried a Miata. I always felt like it was more of a chick car I guess...

 

I always thought of the Miata as the S2000's little sister

 

I actually think that the latest Miata looks like the S2000. Before, they were very different looking but lately it seems like Mazda just upright copied the S styling. I remember once I thought I spotted another S driver going the opposite way but when I got closer it was a Miata

 

I just tell people "yeah it's the 'H' roadster" and point at the honda badge.

I've been asked if it's a BMW, Miata, Ferrari, Porsche, and on and on.