It does have similar formulation but the setting is completely different. Types in Julia are not the same thing as types in statically typed languages with dependent types. In those languages you can elegantly declare the connection between inputs and outputs, and moreover the connection will be checked. In Julia type stability is a property of a code that Julia compiler will discover on its own during runtime. The programmer can't declare it nor have it checked.
> Informally, a function is type stable if the type of the output depends only on the types of the inputs, not their values.
This line reminds me of (the opposite of) dependent-type. But I think that intuition may not be useful or relevant for understanding here?