Difference between Hornady gauge and Sinclair gauge
Both gauges are inherently limited by other factors and cannot be assumed to be telling you the absolute gospel truth about the straightness of your ammo unless all of those other variables are controlled.
Please excuse the kindergartenesk drawings, but maybe this will be helpful.
The cartridge on the left would have good readings from both the Hornady and the Sinclair gauge, because it is concentric both with reference to the overall axis (what the Hornady measures) and with reference to the case wall (what the Sinclair measures). But the cartridge on the right would have good readings from the Hornady gauge (since it is concentric relative to it's axis), but very bad readings from the Sinclair gauge (since it is badly out of alignment relative to the case wall). This shows one weakness of the Hornady gauge if it is used by itself without the Sinclair. But if the case neck is concentric with the case body, the Hornady gauge will do a better job showing whether or not the bullet has been seated crooked, since it fixes it's axis of reference right at the tip of the bullet.