Horse-hoarse merger
The distinction was made in traditional Received Pronunciation as represented in the first and second editions of the Oxford English Dictionary. The IPA symbols used are for horse and for hoarse.
There are of course two sets of words here. Set 1 is made up of most words where the spelling is simply or (fork, horse, morning, north, York) and all words spelled with war or quar (quarter, war, warm, warn). Set 2 has all the words with alternate spellings oar (board, coarse, hoarse), oor (door, floor), ore (bore, core, more), and our (course, mourn, pour), and also many words with or followed by another vowel (boring, glory, oral). However, set 2 also includes several words with an or spelling before a consonant. Most of these are words with a p before the or as in pork, port, Portugal, sport, but it also applies to afford, force, ford, forge, and the past participles borne, sworn, torn, worn.
In John C. Wells's book, Accents of English, 1982, set 1 (horse) is labelled NORTH and set 2 (hoarse) is labelled FORCE.