Interestingly, Sidney does not seem to view these two words as being in opposition with each other, and by contrast, argues that poets both invent and imitate. For example, when talking about the presentation of nature, he states that poets use their powers of invention to "grow in effect another nature," either by improving on nature or by inventing new creatures and beasts. Invention is clearly therefore an important skill of the poet.
However, at the same time, Sidney clearly states that a poet ultimately is an imitator rather than an inventor. He refers to Aristotle to support his argument:
Poesy therefore is an art of imitation, for so Aristotle termth it i the word mimesis--that is to say, a representing, a counterfeiting, or figuring forth--to speak metaphorically, a speaking picture--with this end, to teach and delight.
Poetry is therefore based ultimately on imitation, as it is a representation, or a "speaking picture," as Sidney describes it, rather than anything real. Just as much as poetry relies on invention to improve on nature and create new beings and new worlds, Sidney therefore believes that ultimately it is imitation, as poetry is not real, and therefore it is just a way of "counterfeiting," a presentation of reality that is not real in itself.