high >< low frequency

Core material and physical size.

Switched mode power supplies operate at high frequency so that the transformers (and chokes) can be small ferrite ones rather than big steel ones.

(Del the Cat....not logged in!)

so , much higher frequencies ,

(over 150 Khz dont need an metallic core,

Air coils can transforme any needed Kilowatts.

AM- Transitter (Radio) LW about 200Khz MW about 1 Mht SW about 10Mhz FM 100 Mhz

For understand first steps

look (google) TESLA COIL , Tesla transformer . about 100Kz to 500 Khz typical

Pic of an "bigone"

http://pixerve.de/60240/a-fe-pese.html

Core material & its thickness. Higher the F thinner the core laminations. Power transformers go upto 1MHz now with Soft-magnetic material. After that no core material is used.

It depends on what you call low and high. Low freq. audio and power transformers may be laminated iron core, but a lot of them today use a toroid which is powdered iron or ferrite. Higher freq. audio would use a toroid. For RF applications there are toroids designed for different frequencies. As already mentioned, air core can be used if the freq. is high enough. As the freq. increases, the number of turns drops and the size of the wire and the spacing increases to give the coil a higher Q. Often the coil is wrapped around a hollow ceramic form.

there is not strictly distinguishing between them.

what their core material depends on power dissipate.