The answer is ammonium thioglycolate (thio) relaxer. That's the one you'll find sold in both base and no-base versions.
Hydroxide relaxers are a different chemistry entirely and aren't the ones marketed with a base/no-base split. "Base" and "no-base" refer to whether a protective cream is applied to the scalp before the relaxer goes on, and that packaging distinction runs with thio products specifically — not hydroxide, and definitely not the neutralizing steps that come after either type.
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