This is partially lost in translation. When referring to cosplay here, it is firmly in reference to cosplay as a concept (like the spirit of cosplay), as opposed to cosplay 'things'. The term cosplay does not carry the same connotations in Japanese as it's a made up word. Unlike English speakers who associate the term with "costume" even if you don't know it originated as "costume play", they refer to it as an action or concept first, before it is a noun. Their English literacy is poor, so they don't make the automatic word connection, even if they know about it factually. In that concept, as you guys already know, "cosplay" is referring to embodying that character.
What she refers to here is that normally you "put on clothes", even up to the level of haute couture, and THEN you do "cosplay". But Lilysa's "cosplay" begins with the clothes she makes, therefore Saitoh refers to the making and putting on of the costumes as "cosplay".
Because "cosplay" can be used like a noun and also just refer to the costume in Japanese, like in English, this is difference is a fairly subtle one that comes down to the initial impression you get due to the connotations you perceive. That's why you kind of get it, just that it feels odd. You're forced to switch your perspective, in order for it to make sense, while to a Japanese reader it's automatic.