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The short (snarky) answer is because they are different tubes. . The "5 pin tubes" are actually a 8 pin aka octal base, same as e.g. a 6L6 or 6SN7 but rectifiers only need 4 (or sometimes 5) connections so they save money by only including 5 pins. They all have the center key to ensure you put them in right.

The "4 pin tubes" use an older base, aka UX4, same as a 300B. You can find versions of many rectifiers with either base, i.e. 5Z3 is the 4 pin version of the 5U4G and Type 80 is the 4 pin version of the 5Y3. You can look on ebay for a 4 pin to 8 pin adapter, search for "5z3 to 5u4g adapter". The 4 pin tubes have 2 larger and 2 smaller pins so that is how they are keyed.