As you may know, for most of the Silver and Bronze Ages, the unspoken rule of Batman stories was that the E-1 Batman and E-2 Batman had essentially identical careers as solo heroes (and with Robin). Obviously, elements like the E-2 Batman's battles with Nazis or his mebership in the Justice Society of America remained elements unique to his history, and the E-1 Batman's JLA membership and adventures stayed on E-1 only.
The E-1 Batman would flash back to stories published in the 1940s, stories prior to the "New Look" where he'd be seen in flashback without the yellow chest emblem, and so forth. Thus we got Deadshot and Hugo Strange's returns complete with footnotes and flashbacks to their pre-Silver Age days, and stuff like the "return" of the 1948-model Mad Hatter with a note informing the reader he hadn't been seen since Batman #49.
It wasn't until the late 1970s that DC started deliberately differentiating things. The E-1 Batman was given the history with Lew Moxon as Joe Chill's employer, for instance, while the E-2 (golden age) version had Chill as a random mugger and nothing more. Later writers like Alan Brennert also determined that the latter-day E-1 appearances of 1940s and 1950s debut characters only held on that world. Thus sotries like Brave and the Bold #182 established that E-2's Mister Zero never changed his name to Mister Freeze and that its Hugo Strange had been mangled and crippled by the events of his last pre-Englehart appearance in the 40s.
Now to the Monk: Gerry Conway, who had previously used the indistinction of E-1 and E-2 as had everyone else, decided in the mid-1980s that some of the very early villains (the returned Hugo Strange obviously excepted) didn't have established E-1 counterparts, and started introducing very different versions of them as foes the E-1 Batman had never before encountered. Dr. Death and a significantly altered version of Detective Comics #33's Scarlet Horde turned up in short order; so too did a radically altered Monk, this one given the backstory of a Louisiana plantation owner who so mistreated his slaves before and after the Civil War that they, er, voodooed him and his possibly-incestuous sister into vampirism.
This is quite incompatible with the earlier Monk story for several reasons, not the least being that this Monk is an American and the 1940s Monk had an ancient castle in freaking Hungary. Likewise, the Monk and Dala who attacked Julie Madison had both an entire pack of odd werewolf/vampire types (the Golden Age story didn't really distinguish between the Universal Horror movie archetypes) and were outright destroyed in Tec #32 by Batman shooting them with silver bullets. The E-1 pair were, well, still of the animate variety of unlife, as it were.
Later stories also hint that the 1980s Monk was a radically-different counterpart, not a returning classic model. Roy Thomas's America vs. The JSA series and Len Wein's Untold Legend of the Batman each established that the E-1 Batman, unlike his E-2 counterpart, had never used a gun. Roy also reestablished the distincive 1940s versions of some of the rebooted villains as E-2-only types, with the Conway revamps as E-1-only by default.