I don't know how it's supposed to be in user's language. But in freecad-coder-user language, word "object" usually refers to a DocumentObject, which is anything that shows up as an entry in model tree (apart from "Application" and project entries).
An object may have a shape. May not (e.g. Part containers don't, Groups don't). Some objects don't have shape, yet show up in 3d view (e.g. origin features such as XY Plane). Some objects have no shape and no 3d view representation, e.g. Spreadsheet.
"Feature", when used outside of PartDesign, usually means the same as "Object". In PartDesign, the meaning of the word "Feature" is a bit more specific.