Regarding self as a convention:
If you sit down, you have a lap. When you stand up, where is the lap? Where has it gone to?
What a "lap" is, is just a convention, just a like a "fist".
Similarly, a being (satta), a person (puggala), a chariot (ratha) are all conventions. See SN 5.10.
The self (atta) can be seen in two forms.
In the first case, when am unenlightened person clings to it, it's simply a mental idea (Snp 4.14) in the mind that one clings to.
In the second case, when an enlightened one says "me", "I", "we", "our", "mine", he is just using conventions (SN 1.25).
Even in the first case, it's just a convention too. Why? What you call "self" is somehow pegged to some other concept like your body or your mind or your personality.
So, imagine if you go to the beach and spend a lot of time and effort to build a sand castle. Then someone comes and smashes it. You feel angry and say "why did you smash my sand castle?" "You", "my" and "sand castle" are all conventions. The anger appeared because of clinging.
The concept of "substance" (svabhava) comes in the Madhyamaka philosophy of Mahayana. Madhyamaka states that everything is empty of substance, which means it is empty of the meaning that is given to it by the mind. It's not what you think it is.
Anatta is the notion that everything is not self. The body, the mind, the five aggregates, mental ideas etc. are all not self.
Anatta is a specialized form of emptiness (i.e. everything is empty of a self - SN 35.85), while the Madhyamaka emptiness is a more generalized form (i.e. everything is empty of the meaning given to it by the mind). Both types of emptiness are covered in MN 1. So, Theravada has both too, in fact.
The Madhyamaka emptiness is explained by the Pali term papanca. If papanca is the process of baking, then svabhava is the cake. Please see this answer.
In his commentary to Snp 4.14, Ven. Thanissaro explained that the objectification and classification (papanca) of the mental idea of the self vs. non-self objects, lead to craving, clinging and suffering. He also explained papanca in his commentary to MN 18.
A detailed explanation can be found in this answer.