For those who tend to be visual learners, like I am, here is my understanding of the distinction between those three categories. I am using blazers and sheath dresses from my wardrobe as examples, as those items are the ones I wear often to work, and when in neutral colors and simple cuts are essential for me. In the finds, first row are essential blazers, second completer blazers, and third statement blazers; and the subsequent three rows are the same for sheath dresses.
My essential neutrals are black, navy and white, so 1st and 4th row are my versions of essential blazers and dresses. They are neutral, and the cuts are pretty simple. There may be slight detail, like contrasting buttons on two of the blazers, or modified V-neck on the white sheath dress, but overall the items are still quite simple. These pieces can be supporting actors in many outfits and are not very noticeable.
On the opposite end, we have statements, rows 3 and 6, which are still blazers and sheath dresses, but now there is something very noticeable about them, which could be the cut, color, texture or pattern, or combination of those. They are pretty memorable, and the star of every outfit.
The middle category, completers, are in between items (rows 2 and 5). They are clearly not essentials, as they are perhaps colored or have a subtle pattern, like glen plaid, but there is nothing very noticeable or statement-y about them either, for my style at least.
If you compare the three black blazers, the first one in the first row, essential, is pretty simple overall; the first one in the 2nd row is a moto- jacket/blazer hybrid, so definitely not essential, but there is nothing truly memorable about it for me, thus completer; and the first one in the third row, a dramatic asymmetric cut, is quite a statement.
To my eye, the distinction between essentials and statements is very clear, and the distinction between essentials and completers is not as clear, but pretty close. The line between completers and statements is more blurry, and a bit personal, as to some I imagine a light-mid blue blazer or dress might be a statement, but for my own personal style, they are "average", every-day work clothes, that go well with my eyes. If the same items were in bright red or fuchsia, then they would be statements, as those colors are very noticeable, both in general and on the pale me.
I am not mentioning basics here, as those are undies, lounge wear, socks etc., so there is no such thing as a basic blazer or a basic sheath dress by these definitions.
