Commandments can be thought as something common to the various covenants.
Matthew 19:17-21 (NKJV)
17 So He said to him, "Why do you call Me good? No one is good but One, that is, God. But if you want to enter into life, keep the commandments."
18 He said to Him, "Which ones?" Jesus said, "'You shall not murder,' 'You shall not commit adultery,' 'You shall not steal,' 'You shall not bear false witness,'
19 'Honor your father and your mother,' and, 'You shall love your neighbor as yourself.' "
20 The young man said to Him, "All these things I have kept from my youth. What do I still lack?"
21 Jesus said to him, "If you want to be perfect, go, sell what you have and give to the poor, and you will have treasure in heaven; and come, follow Me."
It can be told here that Sabbath may no longer a valid commandment in the New Covenant. It is because as gentiles we don't keep Sabbath, we attend Sunday services instead.
A typical covenant may have like 4 key components;
1) commandments
2) law
3) grace
4) promises
Commandments may define the core of a covenant,
Matthew 22:40 (NIV)
40 All the Law and the Prophets hang on these two commandments."
Law is for a group of humans under a certain covenant to obey. Today, if you claim to be a Jews by your bloodline, you need to abide by Mosaic Law. Or else you'll be a gentile. As a gentile, you need to abide by the law written in our hearts. This is the default. Every human when born he's subject to one of these two covenants (old covenants) without exception.
When an adult grows up he may choose with consent to be under the protection of the New Covenant. As for gentiles, we have no hope in passing the Final Judgment if we failed to choose the New Covenant by repenting ourselves and put our faith in Jesus Christ.
The New Covenant is with the Law component minimized to zero, and the Grace component maximized to 100%. As gentiles we still need to abide by the Law written in our hearts, even though we are no longer judged that way. However, it is expected that we will inevitably break the Law here and there. It is thus more important for us to follow Jesus Christ's teaching, to be like Him, and to strive for being holy.