The orignal formulation of the "Contradiction" was in the context of the "theory of classes", corresponding (with a certain approximation) to Cantor's original Mengenlehre.

See Russell's letter to Frege (16 June 1902) :

Let $w$ be the predicate: to be a predicate that cannot be predicated of itself. Can $w$ be predicated of itself? From each answer its opposite follows. Therefore we must conclude that $w$ is not a predicate. Likewise there is no class (as a totality) of those classes which, each taken as a totality, do not belong to themselves. From this I conclude that under certain circumstances a definable collection [Menge] does not form a totality. [...]

See also Bertrand Russell, Principles of Mathematics (1903), Chapter 6 : Classes (page 67-on) :

§68. In Chapter 2 we regarded classes as derived from assertions, i.e. as all the entities satisfying some assertion, whose form was left wholly vague. [...] for the present, we may confine ourselves to classes as they are derived from predicates, leaving open the question whether every assertion is equivalent to a predication.

§69. [...] it is plain that when two class-concepts are equal, some identity is involved, for we say that they have the same terms. Thus there is some object which is positively identical when two class-concepts are equal; and this object, it would seem, is more properly called the class. Neglecting the plucked hen, the class of featherless bipeds, every one would say, is the same as the class of men; the class of even primes is the same as the class of integers next after $1$.

§71. Class may be defined either extensionally or intensionally. That is to say, we may define the kind of object which is a class, or the kind of concept which denotes a class: this is the precise meaning of the opposition of extension and intension in this connection.

§73. Great difficulties are associated with the null-class, and generally with the idea of nothing. [...] In Symbolic Logic the null-class is the class which has no terms at all; and symbolically it is quite necessary to introduce some such notion.

§76. Something must be said as to the relation of a term to a class of which it is a member, and as to the various allied relations. One of the allied relations is to be called $ε$, and is to be fundamental in Symbolic Logic.

§77. A relation which, before Peano, was almost universally confounded with $ε$, is the relation of inclusion between classes, as e.g. between men and mortals.

§78. Among predicates, most of the ordinary instances cannot be predicated of themselves, though, by introducing negative predicates, it will be found that there are just as many instances of predicates which are predicable of themselves. One at least of these, namely predicability, or the property of being a predicate, is not negative: predicability, as is evident, is predicable, i.e. it is a predicate of itself. But the most common instances are negative: thus non-humanity is non-human, and so on. The predicates which are not predicable of themselves are, therefore, only a selection from among predicates, and it is natural to suppose that they form a class having a defining predicate. But if so, let us examine whether this defining predicate belongs to the class or not [emphasis added].