Morphology is a qualitative evaluation of the three dimensional shape of a surface, whereas topography provides quantitative feature dimensions. However, I want to know in depth knowledge and Technical difference between them.
Don't mess up topography with topology! By definition, topological properties are invariant under all continuous transformations. In turn, morphological properties are invariant under all rigid transformations and all rescaling transformations (the greek word morphe' means just shape). Hence, any morphological property is also topological, but a generic topological property is NOT morphological: a general continuous transformation may change enormously the shape. Finally, topography completely characterises the geometry of surfaces that admit a topographical description (for instance, a sphere cannot be described by a SINGLE topographical map -- an atlas is needed, consisting of at least two maps).
Why art historians use "topography" instead of "morphology"?
Examine:
Wolfgang Müller-Wiener. Bildlexikon zur Topographie Istanbuls. Byzantion, Konstantinupolis, Istanbul bis zum Beginn des 17. Jahrhundert. Wasmuth, Tübingen 1977, ISBN 3-8030-1022-5.