www.alphadictionary.com

. . . The modern digraph th began to grow in popularity during the 14th century; at the same time, the shape of the thorn grew less distinctive, with the letter losing its ascender (becoming similar in appearance to the old wynn, which had fallen out of use by 1300) and, in some hands, such as that of the scribe of the unique mid-15th century manuscript of The Boke of Margery Kempe, ultimately becoming indistinguishable from the letter Y. By this stage th was predominant, however, and the usage of the thorn was largely restricted to certain common words and abbreviations. In William Caxton's pioneering printed English, it is rare except in an abbreviated the, written with a thorn and a superscript E. This was the longest-lived usage, though the substitution of Y for thorn soon became ubiquitous. The first printing of the King James Version of the Bible in 1611 used the Y form of the thorn with a superscript E in places such as Job 1:9, John 15:1, and Romans 15:29. It also used a similar form with a superscript T, which was an abbreviated that, in places such as 2 Corinthians 13:7. All were replaced in later printings by the or that, respectively. The thorn in the form of a Y survives to this day in pseudo-archaic usages, particularly the stock prefix "Ye olde…". . . .

. . . In Old English, ð was used interchangeably with þ (thorn) to represent either voiced or voiceless dental fricatives. The letter ð was used throughout the Anglo-Saxon era, but gradually fell out of use in Middle English, disappearing altogether by about 1300; þ survived longer, ultimately being replaced by the modern digraph th by about 1500. . . .

Looks like ye olde thorny issue. (Aw c'mon. Someone had to say it. )

Far as I remember, the "hard" one was called "thorn" and pronounced as an unvoiced labio-dental fricative (like th- in today's three. The "soft" one (a voiced labio-dental fricative) was pronounced like the th- in today's the.