This is open to interpretation, and it will depend on context and how the words are being used.
However, consider this:
the actual presence of a representation
"I saw the actor, in makeup, on the stage."
Here, I'm using actual presence to mean something or someone is actually there, and I'm equating representation with an actor in makeup who is representing someone else.
the representation of an actual presence
"I saw a statue, dressed as someone I knew, on the stage."
Here, I'm saying that the statue represents somebody who exists in reality. (The person exists in fact, rather than fiction, despite not actually being on the stage at the moment.)
Note that in order to use those two examples, I had to give a slightly different meaning to actual presence. While the meaning of representation remained the same (either an actor or a statue representing something else), in the first sentence, actual presence refers to the representation being present here and now but in the second sentence, actual presence refers to factual existence of the thing being represented.
Now, let's change the scenario slightly:
"The actor playing the role of my friend was in makeup on the stage, standing next to my friend who was also there."
In this specific scenario, both of the example phrases could be considered accurate and true at the same time.
- The actual presence of a representation could have the same meaning as before—referring to the here and now presence of the actor (the representation).
- the representation of an actual presence might mean the same thing as before, but in this case it could be specifically interpreted as the thing being represented (my friend) being actually present here and now as opposed to just being in existence somewhere.
No doubt the idea of combining actual presence and representation (in any order) is considered paradoxical because of how people might normally interpret them differently than I did. (In order for my examples to make sense, I had to either tweak the normal meaning of presence or propose a presence and a representation coexisting.) Generally speaking, something is either itself or it's a representation of something else. As a standalone sentence (or phrase) where there is no further context, combining the two could be seen in the same incongruous way as the expression the coin toss was heads and tails. In response, people might scratch their heads and wonder how both could be true at the same time.
Also, in broader terms, changing the order of words in any sentence does lend itself to changing the meaning of the sentence:
James attacked Jane.
Jane attacked James.
The woman fell onto the pavement.
The pavement fell onto the woman.
Now is the winter of our discontent. (Shakespeare, Richard III)
Now is the discontent of our winter.
