A right of first refusal is, essentially, a first right to consider an opportunity, before that opportunity can be offered to anyone else. For example, I could say to you that if I ever want to sell my home, I'll offer you the first opportunity (or first right) to negotiate to buy it at the market price. If you reject the opportunity, then I may negotiate and sell the home to anyone else.
By contrast, a right of last refusal is a last right to take up an opportunity, before someone else is permitted to take it up. So, staying with the example where I offer you the opportunity to buy my home. If I promise you a right of last refusal, then I'll need to negotiate with the other parties, agree on the terms of sale with them, and then offer you a final opportunity to buy my house on the terms I have negotiate. If you refuse or reject the offer, of course, I can sell it to someone else, on the same terms I offered you.
Let's look at another example for a First or Last Right of Refusal Agreement. Owen could offer Robert the first or last right to sell Owen's products in Australia. When they sign a Right of First Refusal Agreement, Owen must offer these rights to Robert before Owen can offer them to a third party. If Robert takes up Owen's offer by accepting it, they will have a binding agreement. But if Robert does not accept the offer within the time limit stated in the Agreement, then Owen is free to offer the rights to a third party.
If Robert also has the "last right of refusal" then before Owen can finalise a deal with a third party, Owen will need to check back with Robert and give him a "last right" to accept or refuse the deal before Owen can enter into a final, binding agreement with the third party.
People often ask, "What's the difference between a right of first refusal and a first right of refusal Agreement?"
There is no difference. These terms are used interchangeably.
If you have agreed to give someone a "first right of refusal" or a "last right of refusal", you should document the arrangement in a written Agreement so the terms are in black and white. It helps to clarify expectations and avoid costly disputes.
Similarly, if someone has promised to give you a "last right of refusal" or a "first right of refusal", you should get the arrangement in writing (in black and white) so you can enforce it if they ever change their mind or don't want to honour the arrangement.