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Both seem to be a study of a planet's surface. Topography seems to have more to do with the graphical depiction of surface features, but there seems to be a lot of overlap...

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Topography, in the eyes of Earth Scientists, is the study of the surface features of the Earth (or other planet), and includes all features of that surface, natural or artificial.

From the Oxford Dictionary:

1.The arrangement of the natural and artificial physical features of an area

Topography comes from the Greek topos, meaning 'place'. It is a study of all the features of any specific area, not necessarily just elevation, as depicted in topographical maps.

Orography is a specific study of the features and 'topography' of mountains:

The branch of physical geography dealing with the formation and features of mountains

Comes from the Greek óros meaning 'hill'. Orography can also be known as orology, oreography or oreology... It is concerned with the formation and development of mountains, hills and ranges, for example the formation of a mountain range or ranges is know as an 'Orogeny'. Earth Scientists can refer to groups of mountains or ranges as 'Orogens'.

Orography falls more broadly under the study of Geomorphology, which is not necessarily just constrained to surface features, as in the case of topography.

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