Both tests are more folklore than science!

"The bullet test" depends heavily on the individual bullet contour. One can go in a long way & the other barely at all. It also ONLY checks the crown. Many will tell you its a test for the bore but that's nonsense. For the test to be valid you need a specific single bullet to use as your gauge. Not one similar to another out of the same box, but one exact one. Even then it's an implied measurement, not a solid one.

"Chamber Test" This one opens a whole can of worms. Some things to factor in.

HEADSPACE: The drop a round in won't tell you anything about it at all. The case is rimmed & you have to separate the methodology for Rimless from the one for Rimmed. A lot of stuff has been posted where the two of them have been merged & used where not applicable.

A rimmed case headspaces on the space between the standing breech & the bolt face. NOWHERE ELSE. That's why it measurements are so short compared to rimless cases. 0.067" for the .303 British being "perfect" but anything between 0.064" & 0.074' being "acceptable" (there's also an even sloppier 0.080" "wartime expedient" emergency one allowable! Nothing further forward into the chamber is headspace!

Now there are "chamber variations" & "Generous Chambers".

The case is tapered & the shape of the shoulder taper & neck junction can all vary too. Its also, as has been mentioned "generous" to allow dirt to not bind up or prevent chambering of muddy or corroded ones.

Rimless cases use a "datum line", much further forward, usually the mid point of the taper to the case neck. For them the Headspace is from the closed locked bolt face to this datum line. example 7.62/.308 has a 1.6355" to 1.6455" range.The chamber shape & length to the neck & shoulder are also standardized.

Got a headache yet?

Now some shooters intentionally set the brass of rimmed cases to contact the taper of the chamber, supporting the round by "wedging" the case between the standing breech & the tapered section. It does have some advantages like longer brass life & better alignment in the chamber. BUT there is no "Datum Line" & no single defined contour, so its a unique hand-fit to that exact chamber only.

This is why many Lee Enfield reloaders ONLY neck size their brass. Not full length.

Dropping a cartridge into the chamber doesn’t tell you anything either, except that there is no obstruction in the chamber.  It should drop in, and is stopped by the rim contacting the back of the barrel.  As Shamu said, the .303 cartridge headspaces on the rim.  Rimless rifle cartridges headspace on the shoulder. 

Probably worth getting headspace checked out, unless you already know it’s good. The serial number on the bolt should match the serial number on the receiver.