There is no difference, hi-fi manufacturers use the word monitor as some sort of 'badge' of quality, ie if it is good enough to be used in the studio then it is good enough for hi-fi.
Both domestic and studio speakers can and are built to very different standards and requirements and the differences can be huge. In the pro world the legendary LS3/5A is a true monitor, designed primarily for speach and of a size to fit into outside broadcast vehicles, it is a world away from a pair of recording studio main monitors designed to handle uncompressed feeds from the studio floor.
Full size recording monitors are, unless you are japanese, practically useless in the home. They are designed to produce a wide bandwidth at high sound levels and in normal domestic situations would be far too loud, rattle the furniture and take out the windows (seriously!). In an acoustically treated control room or playback suite they can give a very convincing portrayal of a live musical performance.
The real confusion is the rise of the nearfield monitor of the kind that are found in music shops and sometimes recomended on here. Designed originally for the home or 'project' studio these are usually compact, active designs termed as 'nearfield' monitors only because to be effective as a 'monitor' in largely untreated rooms you need to take the room out of the equation by sitting quite close.
They work perfectly well as hi-fi speakers too, sure, you sit further away and the room has more of an effect but that is the same as for any speaker. The big difference is that such monitors are invariably active and 'sound different' because of that, the power and control that is available, along with other factors, encourage the user to play them much louder than they would normal hi-fi speakers and many hi-fi users hearing this for the first time describe the sound as forward, it isn't, it is just louder than they are used to.
Personally I like the sound of active speakers and, in the main, find them preferable to 'conventional' amp/speaker combinations, particularly at the budget end of the market, say up tp £1500-2000.