For one, Unicode is not an encoding. Rather, UTF-8, UTF-16 etc. are encodings. And a rather common one of them — UTF-8 — is variable-width, i.e. not same number of bytes per character.
Both UTF‑8 and also UTF‑16 as well are variable‐width encodings. The essential difference is the size of the code units. There is an infinitude of Java and Windows code (but not necessarily both) out there that screws this up, thinking that UTF‑16 is UCS‑2. It very much is not so.
Plus UCS‑2 isn’t even a valid Unicode encoding in the first place. UTF‑8, UTF‑16, and UTF‑32 are, and of those, only the last uses fixed‐width code units. UTF‑16 is problematic and annoying in several ways that do not affect either UTF‑8 or UTF‑32, but that doesn’t make it fixed width.
So the same statement as you’ve made about UTF‑8 applies equally well, mutatis mutandis, to UTF‑16: “UTF‑16 is also a variable‐width encoding, i.e. not the same number of 16‑bit code units per character.” It would be very, very good idea to remain ever conscious of this, given how much harm has been done by negligent programmers who have not done so.