I would state that a hack is an undesirable activity with unauthorized access to assets. This can be, but is not limited to, doing an unauthorized action on a private machine such as modifying or transferring data.
This means a "hack" is broader then unauthorized access for most people. When your computer is infected by a cryptolocker, most people would say that their computer was "hacked", even though no access was given to an adversary.
If you take a look at a classic defense model or security landscape, you will see that a user has assets to protect. These assets can be protected by taking security measurements to protect against threats used by adversaries.
Not all adversaries are hackers, just like not all threats are hacking related. Power outage for example is a threat to your assets and you have to take security measurements, but a power outage does not constitute as hacking to most people. This is why it is important to look at threats as well as adversaries.
Depending on your adversary, a fake anti-virus message or browser redirect is a threat to your security (and therefore to your assets) but there is no unauthorized access yet and therefore is not a "hack" in my opinion, rather a malicious action (or threat).