Actually, it feels like swift is trying to promote strings to be treated less like objects and more like values. However this doesn't mean under the hood swift doesn't treat strings as objects, as am sure you all noticed that you can still invoke methods on strings and use their properties.
For example:-
//example of calling method (String to Int conversion)
let intValue = ("12".toInt())
println("This is a intValue now \(intValue)")
//example of using properties (fetching uppercase value of string)
let caUpperValue = "ca".uppercaseString
println("This is the uppercase of ca \(caUpperValue)")
In objectC you could pass the reference to a string object through a variable, on top of calling methods on it, which pretty much establishes the fact that strings are pure objects.
Here is the catch when you try to look at String as objects, in swift you cannot pass a string object by reference through a variable. Swift will always pass a brand new copy of the string. Hence, strings are more commonly known as value types in swift. In fact, two string literals will not be identical (===). They are treated as two different copies.
let curious = ("ca" === "ca")
println("This will be false.. and the answer is..\(curious)")
As you can see we are starting to break aways from the conventional way of thinking of strings as objects and treating them more like values. Hence .isEqualToString which was treated as an identity operator for string objects is no more a valid as you can never get two identical string objects in Swift. You can only compare its value, or in other words check for equality(==).
let NotSoCuriousAnyMore = ("ca" == "ca")
println("This will be true.. and the answer is..\(NotSoCuriousAnyMore)")
This gets more interesting when you look at the mutability of string objects in swift. But thats for another question, another day. Something you should probably look into, cause its really interesting. :) Hope that clears up some confusion. Cheers!