The claim triggers it, not the chemistry
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One sentence on a label decides which of two entirely different regulatory regimes your product is in, and the sentence is the one every cleaning product wants to say.
The same bottle, two products
A multi-purpose cleaner that says it cleans and degreases is a cleaning product.
The identical liquid that adds "kills 99.9% of germs" is an antimicrobial pesticide under FIFRA and must be registered with EPA before it is sold.
Nothing in the bottle changed. The label did.
What EPA actually says
EPA's guidance on this is direct: any product that claims to kill or control microorganisms is an antimicrobial pesticide, and the claim rather than the chemistry is what triggers it.
Which cuts both ways. A product containing a powerful biocide but making no antimicrobial claim is not automatically a pesticide on that basis alone; a product containing nothing but soap that claims to kill germs is making a pesticidal claim it cannot support and has not registered.
The second of those is the common case, and it is usually accidental.
Why this surprises people
Because "kills germs" is the most natural thing in the world to put on a cleaner, and because the entire consumer category is built on that language.
The large brands making those claims hold registrations. A small maker copying their label copy has copied the claim without the registration behind it.
It also surprises people that the regulator is EPA. A cleaning product feels like a consumer goods question, and the moment it claims to kill something it becomes a pesticide question.
What it costs to be on the wrong side
Selling an unregistered pesticide is a FIFRA violation, and the enforcement reaches the manufacturer and in some circumstances the seller and the user.
It is also the kind of thing a retailer's compliance team checks before taking a line, so the commercial consequence usually arrives before the regulatory one.
Two honest routes out, and the rest of this section is those two: register, or write the label so the product is a cleaner.