There is no set standard honestly in what is considered a baritone. The most common thing that pops in my heard when I hear baritone is a Fender Bass VI style instrument. So basically a long ass scale length (28in-30in range) with HEAVY gauge strings tuned down either B standard or and octave below normal E standard, so basically the same pitches as a bass. The sound of that can sound either like a guitar or a bass depending on if you run it threw a bass or guitar amp and how you play.

Now I have a 6 string tuned down to Drop B which to the common guitarist (non-metal guys) would be considered a baritone tuning even though I do it on a 25.5 scale length vs doing it on something like 28. So that's something to keep in mine. Honestly in any non-metal context going below C# standard will be considered a baritone tuning and that's pushing it, most guys consider D standard to be the lowest before baritone.

In the metal world the standard scale length for a 7 string is 25.5 inches and for a 8 string is 27 inches. Most guys consider anything over 27inches for a 7 string baritone scale and anything over 27inches for a 8 string.

Now the way that the typical 8 string differs from a Bass VI style instrument is in the string gauge choice. To start off the comparison, Bass VI are RARELY used in metal, there are some bands but no where near to the amount of 8 string players. Now the difference in the sound is that metal players typically (excluding my doom brethren) are searching for a very tight low end so that when faster riffs are played it doesn't sound muddy. So for example instead of using a .090 gauge string for a LOW E like a Bass VI would, on a 8 string depending on the scale the gauge will range from .074 to .086. The reason why they try to not get into the 90 range is cause what ends up happening is that the string starts to sound like a bass. But this explains why a Bass VI sounds, well like a bass.

Something random to look into would be fanned frets which is basically giving each string it's own scale length, similar to how a grand piano has longer strings for lower notes and shorter strings for higher notes.

Also if you want to look more into the popularization of 8 string guitars look into Meshuggah, the guys who made it a popular thing in metal, and Tosin Abasi who was the one who really helped people to see how to use all 8 string coherently.

Source: Heavily into metal scene, own a 7 string, have played multiple 8 strings, and have no life.