I was recently thinking about cyberpunk-2020 and how much I'd like to update the game while maintaining the features I like best about it. This led me to realize if I did embark on such a system overhaul I wouldn't know whether to call it a hack or a clone? Is there a difference between the two and if so, how so?
In general, a Hack seems to be understood to be the taking of a system and tweaking it to use the system for something that was not necessarily originally intended. In general, these are partial changes that do not include a full ruleset, but instead the relevant portions to make it work (though these are sometimes repackaged- sometimes even commercially- to become a full rule set, i.e. Dungeon World).
For some examples to point the way towards what hacks might be (in reference to Apocalypse World): The Big List of Apocalypse World Hacks
The term Clone in general has seemed to be taken to refer to the taking of an older system and making a tribute to the original ideals and flavor while updating and/or modernizing the mechanics to make it more digestible to a different audience.
For some examples to point the way in regards to what a clone is (in reference to AD&D) : A Master List of D&D Retro Clones
All that said, I think it's a matter of individual preference more than actual nomenclature, though I'd probably call what you're doing a Clone more than a Hack.
Neither of these terms are explicitly defined anywhere. However, we do see some precedent for such things in other communities.
If one takes, for example, 1km1kt, the term "hack" is used to describe someone turning a system or game away from its usual intent/genre/style. As 1km1kt is a community for free and/or openly licensed games, hacks are not unknown.
One thing to note is that in almost very case, hacks are typically not officially licensed or supported. In many cases hacks do not have to be stand-alone; for instance, many Savage Worlds settings can be called "hacks". Much like clones, hacks typically include their own rule and setting information.
One important thing to note about hacks is that while they typically try to maintain some rules coherence, they do so for practicality more than for a particular sense of reverence for the original game (which is not to say that none exists).
Clones, on the other hand, almost always refer to a fairly faithful adaptation of one system in a modern format. They are often undertaken as an act of love, though few are official sequels to the original work.
Clones are often as much about nostalgia as they are about building upon great game principles; they're about making a game that feels like an old classic. Note that this is not meant to degrade clones; many are great games, but they prefer similarity to the existing rules over improvements.
There are some clones, however, that greatly modify the content that inspired them; look at Stars Without Number for an example.
A general basic idea of a hack versus a clone is that a hack says "Wouldn't it be cool if X did Y?" while a clone asks "How would X do this?" for any added content, and clones tend to focus more on making the original experience of a game available again where hacks seek to make something new.