A machine has moving parts and is capable of 'doing' something, although usually needs human guidance (a 'driver'). The equipment is the set of tools used by a human being for a specific task. The equipment needed to fix a car might consist of hand tools plus machines. The equipment needed to write a single love letter usually does not include machines in it, being just pen, paper and possibly an hard surface. The equipment needed to write 3 million letters to send to the tax-payers in order to raise money usually have machines in it (obviously bought with previous tax money).

A machine works mechanically, of course. :) Equipment has a wider definition and refers to things needed for a certain task. So this may mean machines, but can also include other tools and even clothing. For example, "mountaineering equipment" would include ropes and carabiners.