It links to Wikipedia (WP), which defines "system" by:
> a computational system (such as an abstract machine or programming language)
there is no better citation[0], because it's not true under some definitions of "computational system", per WP's definition of "computational system" [3]. For example, under the WP definition of "abstract machine", a non-computable function satisfies the definition. Or we can define it as follows: input: strings in an alphabet A, output: {true, false}, operations allowed: check for membership in a language L in alphabet A.
So we see that theoretical formal languages are a subset of computational systems. But there are uncountably many formal languages and only countably many TM. Crucially, we can easily turn each language into one that acts as a universal turing machine while still being distinct. Hence there are uncountably many Turing-complete languages for a given alphabet A[2]
[0]: incidentally, the linked WP page claims slightly differently (unimportantly) that "All known Turing-complete systems are Turing-equivalent, which adds support to the Church–Turing thesis."
[1]: "A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter." Absent a more precise definition, I assume the set may include arbitrary mathematical operations (and it is useful to define non-computable abstract machines, and in general usage in the field abstract machines may refer to languages more powerful than Turing machines).
[2]: Sketch: Let U' be a Universal TM in alphabet A (hence U is Turing-complete), let M' denote the language it accepts, and let 0 be a symbol of A. Define M such that if i' in M', then i in M, where i is i' with every symbol duplicated and 0 prefixed (hence if i'="123", i="0112233") Define N such that if i' in complement(M'), then i in N, where i is i' with every symbol duplicated and 0 prefixed. Observe that every language disjoint from N that contains M is Turing-complete (wrt a slightly modified description for TMs and the simulated input than the one for U'). Now, let L be an arbitrary language in A. Define f(L) = { j | j' in L, j is j' with every symbol duplicated }. Then we see that f(L), M, N are all disjoint. And if T, U are distinct languages, so (f(T) union M) and (f(U) union M) are distinct languages that simulate Turing machines (i.e. they are Turing-complete). Hence there are uncountably many Turing-complete languages. There are only countably many Turing machines, hence only countably many Turing-equivalent languages, so in fact most Turing-complete languages are not Turing-equivalent languages.
[3]: of course,