PokéBase - Pokémon Q&A
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Pokémon Base Set was the first set of Pokémon TCG cards released in
the United States. These cards were printed by Wizards of the Coast .
The first print run of a set would have a special “Edition 1” logo on
the left side of the card, just below the card art.

Just because they are from base set doesn't make it a first edition card.
This is because they are later printings of the same set.
(being rarer also raises the price but that's not a card difference aesthetically)

Picture for reference: base set and first edition Charizards