Some terms are in general use, others probably come from dreamland and are just confusing.
Electrical machines can be radial or axial depending on the direction of the flux path.
Most conventional machines are radial with the flux flowing in the radial direction.
A small number of commercial things using modern magnets are axial such as pancake motors. The axial construction seems mostly to be home built stuff as it removes a lot of mechanical constraints on the construction.
Traditionally for 100 years machines have been iron cored with the coils wound in slots.Some of the the very early ones were air cored (no iron) but the electromagnets of the day made this construction unattractive, with the coming of neodymium magnets it has now become more practical and has some advantages for wind power.
Magnetically levitated I had better not comment on its about as useful as your last one Etc.
Efficiency and economy are closely linked and generally the aim is more towards cost effective than the ultimate efficiency. Efficiency in a wind turbine alternator can be very confusing and striving for the highest efficiency may cramp your style.
Most electrical machines are designed for high efficiency at full load but wind things rarely run at full load so you may do better with high efficiency in low winds where power is scarce. This is one reason why air cored machines can compete with iron cored ones for wind and not generally for other forms of power generation .
Flux
