Are front and rear 51mm post mount calipers the same?
Pretty sure they are but just want to confirm.

good question! 🙂

I do know, now that for a given post mount, an IS-post adaptor for the front 160mm cant be used on the back, and a 160mm IS-post adaptor on the back is the same as an IS-post adaptor for 160mm on the front.

Shimano do an LX calliper which they call front and rear (they are identical, post mount calipers, except for the two different adaptors to convert them to IS front and rear) which they provide with the right IS-post adaptors, but whilst the front would work at 160mm on a post mount fork with its adaptor taken off, I have no information as to whether the same would apply to the rear one…but Im guessing it ought to 🙂

I do know, now that for a given post mount, an IS-post adaptor for the front 160mm cant be used on the back, and a 160mm IS-post adaptor on the back is the same as an IS-post adaptor for 160mm on the front.

That didnt make sense!
You mean for the same IS-post adaptor, the rear disc will be 20mm smaller.

The calipers are the same, using different adapters to swap between disc sizes/mounting systems.