Answer:
In casual everyday speech, those three words could refer to the same kind of thing. However, the connotations and denotations of the words do differ. I will speak to the connotations, as the definitions can easily be accessed in any dictionary.
Equipment speaks to being in a certain place and doing whatever you need to do there. To do what you want, you must equip yourself with the necessary items. Think snow gear, water gear, desert gear etc. Each item prepares you for the conditions of the environment. Or, think of audio equipment. You are either in a studio or a venue, and there are many pieces of equipment designed to do pretty much anything you want to do in that setting. Studio equipment is best at capturing a sound. Venue equipment which is known as live gear is designed to amplify, mix, and augment the performance.
Tools speak to doing a specific task such as building, fixing or demolishing. Tools are really everywhere. For tools, there is implied a specific purpose and time where that happens. A builder uses his tools when at work. Every building was built with tools at some point. Everything being fixed by tools has broken down at some point, and after being fixed, will no longer require the tools that did the job. Unless it breaks again. This is the main difference with equipment, which is intended to be used at any time and can be used for non-constructive purposes. The meaning is close, but “equipment” is more broad than “tools”.
Device speaks to practically anything you want, and is very broad and general. It isn't as general as the word “thing”. Devices do something that they were created to do. A device tends to be something technological, although it can be only vaguely so. A door can be described as a device, but not a tool or equipment. A shovel is a device or a tool, but not equipment unless you are a gardener or farmer. A studio reverb plate is equipment, and a tool, and a device.
