Do these words mean very specific things? Are they all the same? What are the defining factors?
A buck converter is a circuit that reduces an input voltage to a lower voltage with a higher current capacity.
A boost converter or step-up booster increases an input voltage to a higher voltage with a lower current capacity.
Those two terms are circuit descriptions and may be parts of more complex equipment including power supplies. However they be applied as a shorter version of something like "boost converter power supply"
A power supply is a product or circuit that receives input power at a voltage that may not be well regulated and delivers power at a voltage or current that is usually well regulated. If the output is not regulated the term unregulated power supply is usually applied. A power supply may be adjustable and often has protective features such as current limit for a voltage supply and voltage limit for a current supply. It may have fuses, a circuit breaker, over-temperature protection. Power supply products may have connectors of a type that would not be used if they were built into a product. A power supply in its own inclosure would usually be called a workbench power supply, but that is usually shortened to bench supply or just power supply.
A buck converter takes a voltage and outputs a lower voltage. A step-up booster takes a voltage and outputs a higher voltage. A power supply is a more generic term for either of these.