The difference between two terms like this can often quite be complicated to understand. However, the key thing to recognise about these two literary expressions is that irony is a literary technique whereas satire is literary form or genre. Therefore, when we think of these two terms we need to bear in mind that we are thinking of two separate things. Satire is a literary form that, by its very nature, contains a great deal of irony which helps it achieve its purpose of holding various aspects and actions of society up to ridicule. If you think of a famous satire such as Jonathan Swift's "A Modest Proposal," you can see how this functions as the speaker of this text ironically suggests the slaughter of Irish babies to "solve" the problem of the Irish famine. The irony in this satiric text is aimed more at the way in which the English were doing their best to ignore this disaster, thereby exposing their inhumanity.
Irony is therefore separate to satire. Whereas satire is a literary genre that is inseparable from irony, and relies on irony to achieve its purpose, irony is a technique that can be found in any text, not just satiric texts. Irony is any situation where there is a massive difference between what is said or seen and the actual reality of the situation, and is therefore used to exploit the differences between appearance and reality.