Why is Unevaluated[#]& different from Unevaluated?

I thought that for any function f we could use "f" interchangeably with "f[#]&".

That is only true if the function has no special attributes. Function effectively removes those attributes, and all other special behaviour.

For example,

Hold[1 + 1]
(* Hold[1 + 1] *)

Hold[#] &[1 + 1]
(* Hold[2] *)

Function[x, Hold[x], HoldAll][1 + 1]
(* Hold[1 + 1] *)

(For the last one, see the 3rd argument of Function.)

Please read Evaluation of Expressions at least up to Nonstandard Evaluation. As I remember it should contain the answers to your question.

The two are not equivalent. Even if f lacks special attributes.

Assuming no special attributes are present, a function's arguments are always evaluated before the function is called. This event occurs twice with f[#] &[x], but only once with f[x]. Now, if everything has been fully evaluated, then you won't see a difference, but if something is marked as "do not evaluate", then you can see a difference.

(This can be very counter-intuitive if you're only used to traditional programming languages.)

Here's a counterexample:

Print     [Unevaluated[2 + 2]]      (* prints 2 + 2 *)
Print[#] &[Unevaluated[2 + 2]]      (* prints 4     *)

However, I think (though I'm not 100% sure I've considered all the cases) that the following two would be equivalent if f lacks special attributes:

f
f[Unevaluated[#]] &

The head Unevaluated is a symbol with the HoldAllComplete attribute. The head Unevaluated[#]& is not a symbol and thus has no attributes to suppress Mathematica's evaluation of its tail.