Base, basis, foundation, ground, groundwork are comparable when meaning something on which another thing is reared or built or by which it is supported or fixed in place.
Base may be applied to the lowest part or bottom of something without strong implication of purpose as a support or prop, but more often it implies specific reference to a broad bottom or to a substructure on which a thing rests or seems to rest for support or by which it is kept upright or stable.
The word may fail to stress an underlying and then applies to something which serves either as a starting point of a development, an operation, or a process, or as a necessary ingredient that carries or contains the active ingredient of a mixture.
Basis like base may be used in reference to something that underlies and supports or to something that serves as a starting point, but the term is rarely applied to a physical or material thing; thus, one may speak of the base (but not the basis) of a monument, or of the basis (not the base) for a certain belief.
Foundation usually implies solidity in what underlies and supports and fixity or stability in whatever is erected on that support; thus, a house has a base even if it rests directly on the ground but it may properly be said to have a foundation only when it rests on a substructure (as a wall of stones or bricks lining an excavation and usually rising above the surface of the ground); a report may be said to have its basis (not foundation) in speculation, but a report that is said to be without foundation has no basis in fact.
Ground implies something solid or firm beneath, or a substratum comparable to the earth or ground in its firmness and capacity for support; the term is therefore applied to a material, a substance, or a surface upon which another thing is built or against which it is displayed; thus, a piece of net may serve as a ground upon which a pattern is worked in lacemaking; before a decorative design is applied to a wall, the ground, or wall surface, must be treated and colored so that it will take the pattern and display it properly.
Groundwork is applied not to a substratum but to a substructure; like foundation, the term suggests something built up before the superstructure is erected, but, unlike foundation, it is used chiefly in a figurative sense.