Why the 4.7-inch variants did not share ammunition freely

Were shells interchangeable between the Royal Navy's different 4.7-inch guns?

Only imperfectly: a shell from one system might theoretically fit another in one direction, but the reverse was unsafe and a proper common round would require further development.

Nominal bore diameter did not guarantee genuine ammunition interchangeability. The 4.7-inch weapons on screen used different gun and cartridge arrangements, so a round that might physically enter one system was not necessarily safe or useful in the other. Compatibility was one-way at best, and a common round would still need development work. Ammunition engineering was therefore part of the standardization problem because the Royal Navy's 4.7-inch weapons were not identical.