'Horn' is an ambiguous term really as it means two entirely different things. To my mind "proper" horns are front-loaded, e.g. Klipsch, Altec, Avant Garde etc, and the best are fully horn-loaded (i.e. they don't have direct-radiating bass). For size constraints many speakers are kind of half-horn-loaded, e.g. Klipsch Heresys, Cornwalls, Altec 19s etc in that the top/top & mid is a compression driver and horn, the bass is a conventional direct radiating box. Then we come to designs such as Lowthers, Frugal Horns etc which to my mind are far closer to transmission-lines in that the horn aspect is just a means of back-loading the bass driver and the treble and mid is just standard direct radiating like any other box speaker. There are good and bad examples of all variations, but my mental image of "a horn speaker" is a Klipschorn, La Scala, Western Electric cinema horn etc, i.e. all front-loaded horn.
PS Jonathan, just pop round if you want to hear a pair of La Scalas. Mine is not a perfect audiophile installation by any stretch, they are just parked in deep alcoves and are my TV system, but they sound pretty decent driven by my little 2.3 Watt Decware.