While the existing answer is mostly correct, it's missing detail on glitch Pokemon, which is what the asker is interested in. So in this answer, I'll explain what glitch Pokemon are in Gen I, and how they're different from Missingno.
Missingno. isn't really a traditional glitch Pokemon, because it was an intentional addition by the developers. By definition, a glitch is a programming quirk that was unplanned for and was never intended by the developers. That's certainly not what Missingno. is. Missingno. is, more or less, a data filler. I'll get more into that later.
If you're at all interested in what Missingno. actually is, please read this fantastic article. This will explain everything about Missingno., from why it exists to why it registers Cubone as seen in the PokeDex. You may not be ready for the terminology, but it's still the most useful guide out there even if you don't understand it.
As for the rest of this actual question, I'm going to answer it in a sequential dot point form, because it's easier to explain that way.
- Pokemon are organised by "index numbers" in Generation I, which are unseen numbers that game uses to identify Pokemon. It's easier to simply think of these as an alternate version of the PokeDex, but with some significant changes. Pokemon appear randomised in index numbers, and do not follow the PokeDex order that we're familiar with.
- The first generation games are capable of referencing, or "looking up", 256 different index numbers (from 0 to 255).
- Of those 256 index numbers, 190 are "slots" reserved for actual Pokemon. Now, as we know, there are only 151 actual Pokemon. This is where we encounter issues.
- The remaining 39 slots of those 190 are all different forms of Missingno. Yes, that's right, there are 39 different versions of Missingno. (explains why some appear with different sprites; certain index numbers reference a Missingno. with fossil sprites or the Lavender Town ghost).
- Why there are 39 extra slots of data intended for Pokemon, but ended up as placeholder Missingnos, is debated. However, all evidence suggests that these were scrapped ideas for Pokemon, all of which made an appearance in Gen II. The developers were forced to put something in place of those Pokemon, so the created the aptly named "Missingno.", because those index numbers are literally "missing numbers". So for that reason, it's reasonable to say the 39 versions of Missingno. are all just formatted Pokemon data.
- The fact that there are 39 Missingno. index numbers should be OK, because the game is never told to reference any index numbers that are a Missingno. (e.g. 31, 32, 50, 52 etc.) However, by exploiting bugs such as the well-known Old Man glitch, it is possible to "force" the game to reference those Missingno. index numbers. That's how you encounter Missingno., the 39 Pokemon you were never supposed to see.
- Back to those 256 possible index number references. What happens if the game references one of the 66 remaining index numbers? You get true glitch Pokemon. You can see these on this Bulbapedia article, which refers to those numbers as "garbage data", which is essentially what these glitches are.
- So really, there is no "original identity" for those 66 glitch Pokemon, because they were never supposed to exist. Their identity is the 66 remaining index numbers that the developers had no data for. That's it.
A brief overview to conclude: Missingno. is (most likely) formatted data from scrapped Pokemon that didn't make it into the game. Missingno. is not a glitch. True glitch Pokemon are the ones found in index numbers 0 and 191 to 255, which were not intentional additions to the game.