I interpret "slip" to require pressure, while "run" means under the gauges own weight.
When I thought I was a real enfield collector, I carried .301" & .302" BSA bore gauges and a .300" diameter pin gauge.
Many No4 and No4T rifles I examined barely accepted the .300" diameter pin, .301" certainly wouldn't "run" thru most of them.
For a while, I only bought rifles which would not accept the .301" gauge at the muzzle.
Now I don't worry about it, if the bore and throat look OK, they are OK. Real problems are usually easily seen.
No1 rifles would sometimes "run" under their own weight with quite large diameter bore gauges...and they still shoot fine.