There's actually no formal distinction between 'hill' and 'mountain', although in some parts of the world practical definitions which include height restrictions are implemented for legislative/legal purposes. For the purposes of 'Right to Roam' legislation in England and Wales, for example, "mountain" is defined as all land over 600 metres.


In common usage a 'mountain' is generally considered to be steeper than a 'hill', and has a clearly distinguishable peak. But again, usage varies.


In actual fact, the only thing which makes a prominence a mountain rather than a hill is the fact that at some time, somebody named it "Mount something or other"