European beech
See en.wikipedia.org

The dominant species include ... beech ... (AB ev) (Fagus sylvatica)

The forest comprises pure stands of beech Fagus sylvatica at lower altitudes and mixed stands of beech and fir Abies alba higher up. (UNEP-WCMC)

Ordesa and monte perdido: "At elevations up to 1,000-1,700 meters, there are extensive forests of beeches (Fagus sylvatica), Abies alba, pines (Pinus sylvestris), oaks (Quercus subpyrenaica), and a lesser extent of birches (Betula pendula), ashes (Fraxinus excelsior), willows (Salix angustifolia)."

"crowned by green beech tree forests on top" (OUV statement)

Southern beech

Southern beech (a separate family from the other European / Asian beeches, but within the same Fagales order).
See en.wikipedia.org

Japanese beech or Siebold's beech, native to Japan
See en.wikipedia.org

At lower levels between 1,000 and 1,500m, some broadleaf forest mainly of beech Fagus sylvatica, covers 5% of the Park (UNEP-WCMC)

"The mountain zone (mainly falling within the core zone) is generally referred to as the "beech belt" but on Etna, where the beech is at the extreme southern limit of its distribution range, it is spread in a very fragmentary way. The present beech woods on Etna can, in fact, be considered relicts of the much bigger formations which were widespread in the post glacial period when the climate was colder and wetter. (...) These beech forests in Mount Etna reach the highest altitudes ever recorded in Europe, and at the same time they represent the most southern location (the lowest latitude)." (Nomination file, p. 59-60)

beech Fagus sylvatica forest above 700m (UNEP-WCMC)

Nothofagus beech forests

the largest and most contiguous primeval beech forest in the subtropical region (AB ev)

The Colchic forests comprise several types of vegetation, among which the East-Euxinian beech forests and oak forests that alternate with hornbeam-chestnut-beech forests. (Nomination Text, p. 23)

Subantarctic or Magellanic forest dominated by the cold-hardy southern beech, Nothofagus (UNEP-WCMC)

"Dominated by a number of Southern Beech species" (AB ev)