What is the difference between non-self and emptiness? Non-self (anātman) and emptiness (śūnya or śūnyatā) are very similar aspects of the Truth of Suffering. So similar that they are hard to distinguish apart. What is the difference between them? (Or what is purpose to have them as separate characteristics?)
Update: I did not specified that answers should be from Mahayana perspective, assuming that Theravada have the same list of 16 Aspects of Noble Truths, but it seems that Theravada list is quite different (see Visiddhimagga). And for some reason most answers was from Theravada perspective. I don't want to disregard Theravada explanations, and welcome them. But in Theravada, it seems, that suññata and anatta are never enumerated in the same list. Thus they don't imply distinction, and it's is quite possible that they are just synonyms (as pointed out by Unrul3r).
I will quote Abhidharmasamuccaya for more context:

What are the general characteristics of suffering? They are the
characteristics of (1) impermanence (anitya), (2) suffering (duḥkha),
(3) emptiness (śūnya) and (4) non-self (anātma).

Thus it's established that these are different characteristics.
Further Asanga provides some elaborations:

(3) What is the characteristic of emptiness (śūnyatā)? It is the
non-existence (abhāva) of a certain thing, there. To see
(samanupaśyanā) in this way is emptiness. Again, it is the existence
(bhāva) of another thing, there. In this way there is true knowledge
(yathābhūtajñāna). This is called emptiness perceived by penetration
(avatāra). True knowledge denotes the informed meaning. What is the
meaning of the non-existence of a certain thing, there? It is the
non-existence in the aggregates, elements and spheres of a self or
anything whatsoever belonging to a self of permanent, durable,
eternal, immutable nature. In this way is their emptiness. What is the
meaning of the existence of another thing, there? It is the fact that
there is non-self in the aggregates, elements and spheres. It is the
nonexistence of the self, and the existence of the non-self. It is in
this sense that the Blessed One has said: ‘Existence is the true
knowledge of an existent thing; non-existence is the true knowledge of
a non-existent thing.’
(4) What is the characteristic of non-self (anātma)? It is the
non-existence in the aggregates, elements and spheres of the
characteristics postulated in the theory of the self (ātmavāda) as a
result of the nonexistence of the characteristics of a self in the
aggregates, elements and spheres. This is called the characteristic of
non-self. For this reason the Blessed One said: ‘All things (dharmas)
are without self.’122 Furthermore, the Blessed One has said: “(i) All
of that is not mine, (ii) nor ‘I am’ nor my self”.123

So in light of this, what is the difference?
As I understand, Mahayana's shunyata (noun, because shunya is adjective) includes all Three Characteristics of Existence, as well as Nirvana (sometimes counted as the fourth!)

In this sense, Shunyata is the all-encompassing view, and as close as it gets to Ultimate Truth, while Anatta is but one aspect of this truth.