Those four-letter codes are not gratuitous jargon: they describe exactly how the transformer removes its heat, and how much power it can hold.
A transformer dissipates its losses as heat. It is that heat, and the temperature it drives the insulation to, that limits the power the unit can deliver continuously. The better it removes heat, the more it can carry. The cooling mode describes precisely how that removal happens.
For an oil-immersed transformer, the code follows the IEC logic (IEC / EN 60076-2). The four letters describe, in order:
For a dry-type transformer, the codes are AN (natural air) and AF (forced air).
A transformer can be specified ONAN/ONAF: it carries one rating in natural cooling (ONAN), and a higher one when the fans kick in (ONAF). Very useful to absorb peaks or hold a reserve, without permanently oversizing; data centers use it to unlock a phase-two rating, as described in the data center guide. It is stated at sizing stage.
For classic distribution, ONAN is enough. Move to ONAF when you want a power reserve or need to manage peaks; to forced cooling for very high ratings. The right mode is set together with the power and the load profile; see the sizing guide.
General overview; the final cooling mode is determined with the power, the environment and the load profile.
Oil Natural, Air Natural: oil circulating by thermosiphon, cooled by ambient air with no fans. It is the standard mode for oil-immersed distribution transformers.
ONAF adds fans on the radiators. The same transformer can then deliver more power while the fans run, useful for peaks or as a reserve.
Two ratings in one machine: one in natural cooling, a higher one with the fans on. You keep headroom without permanently oversizing.
The codes are AN (natural air) and AF (forced air): forced ventilation likewise raises the permissible power.