What standards do MIL-DTL-38999, MIL-DTL-26482, and MIL-DTL-5015 refer to, respectively? How should one choose between them?

These three major military-standard series are currently the most widely used military circular connector standard systems in the world:

MIL-DTL-38999 (main standard)
Full name: MIL-DTL-38999 Grommetless Rectangular and Circular Rack and Panel Connectors
Positioning: High-performance circular connectors, most widely used in aerospace
Four sub-series:
Series I — Bayonet locking, low profile, vibration resistant
Series II — Bayonet locking, flame-retardant housing
Series III — Threaded locking, mainstream model, best cost performance
Series IV — Threaded locking, with shielding and filtering function
Typical applications: aircraft avionics systems, missile systems, radar equipment

MIL-DTL-26482
Positioning: General-purpose circular connectors, cost-effective
Two sub-series: Series I (bayonet) and Series II (threaded)
Typical applications: industrial equipment, ground vehicles, communications equipment

MIL-DTL-5015
Positioning: High-current circular connectors, mainly for power transmission
Typical applications: power distribution, industrial machinery, ground support equipment