Substantially means to a large extent. Substantially higher, substantially complete, substantially the same.
In contracts it is doing exact work rather than vague: substantially complete is a defined stage at which a building can be used and the money falls due. Substantially the same means the differences do not matter.
1adverbsubstantiallyTo a large extent.
“The new edition of the book is substantially longer than the first.”
substantially is a degree.
Latin
substantiālis
Old French
substanciel
Middle English
substancial
English
substantial
English, today
substantially
From substantial + -ly. substantial comes from Middle English substancial, substantiall, from Old French substanciel, substantiel and its etymon Latin substantiālis.
Etymology from Wiktionary, CC BY-SA