Mercy and grace are sometimes used interchangeably, but it can be helpful to make a distinction between the two. Mercy is not getting the wrath that we deserve. Grace is receiving blessings that we do not deserve. Here's an example. God was commanding Moses to go to Pharaoh and deliver a message for Him. Moses hesitated, saying that he doesn't speak very well. And even after God assured him that wouldn't be a problem, Moses still asked Him to send someone else. Then, we read,
Then the anger of the LORD was kindled against Moses and He said, "Is there not Aaron, your brother, the Levite? I know that he can speak well..." (Exodus 4:14)
What's notable in this verse is that God was angry with Moses for Moses' complaining about what God had commanded him to do. But rather than God's destroying Moses and moving on to someone else (mercy), He actually provides for someone else to speak on Moses' behalf (grace). He didn't give Moses what he deserved and instead gave Moses what he did not deserve.
The same is true for all of us. God does not give us the wrath that we deserve. He shows us mercy. And He gives us the most amazing grace of all: forgiveness and eternal life through faith in Jesus Christ.
Even to unbelievers He shows mercy and grace. He does not destroy them immediately, and He allows them to enjoy many of the blessings on this earth, what theologians call "common grace". And yet, there will be a time where His mercy and grace toward them will run out. He will then display His justice, by punishing all those who have sinned against Him and did not trust in Jesus Christ.
But that time is not yet. Even now, trust in Jesus and be forgiven of your sins (mercy) and given eternal life (grace).