Gen 1 Beta Pokémon 

All Beta Pokémon are born with the BETA title, which is visible within your Pokémon's inventory listing. (Ex. LVL5 PKMN [β-Honoguma | Default | BETA])
Non-beta Pokémon, such as Bulbasaur, can only get the BETA title through being born from another Pokémon with the BETA Title or added with the use of a special item (Not revealed yet).

Within ONLY the Beta-Pokédex pages, a [ β ] beside a name represents a non-beta Pokémon with the BETA Title.

For example:
"Ivysaur [ β ]" is the same thing as "[Ivysaur | Default | BETA]"
It is an Ivysaur with the BETA title.

The BETA title allows the Pokémon to access any Beta's within their lineage, such as
- Evolving into a Beta Pokémon
- Devolving into a Beta Pokémon
- Showing design elements of a Beta through the intermediate trait.

Examples:
[Pikachu | Intermediate | BETA] would be able to show Gorochu design elements with the intermediate trait.
[Ivysaur | Default | BETA] would be able to evolve into Beta Venusaur
[β-Nyōsuka | Default | BETA] would be able to devolve into [Poliwhirl | Default | BETA] 

Additionally, All betas that never got finalized into an official Pokémon (Such as β-Kakoroach, β-Cervarro, etc) will have a "β-" next to their name to inform the user that they are a Beta Exclusive Pokémon. Any who got finalized into an official Pokémon, such as Beta Venusaur -> Venusaur, will NOT have this symbol. 

To evolve a Beta, you must use a Prehistoric Fragment.

Sources: The Cutting Room Floor, pokemon.fandom.com, Bulbapedia