We measure all wheel diameters on the tread. Some other manufacturers measure wheel diameter over the flange. When comparing prices do double check what dimension they are using.
Our axles for 7¼" Narrow Gauge and 10¼" gauge all have generous stress reducing fillets where there is a change in section. All our 7¼" narrow gauge and 10¼" gauge wheels are machined with a fillet on the rear face to match. Why do we do this? We've had to remove broken axles in the field (lying in the mud with a handful of spanners, in the rain...) and failure has always been due to a sharp stress raiser where the axle diameter changes just behind the wheel.
All our standard wheels and axles are produced with an interference fit. So, wheels require press fitting or shrink fitting onto axles. We can normally supply wheels ready assembled onto our axles if you are unable to do this!