Yup. Grade of concrete denotes it's characteristic strength.
M10, M15 and M20 are known as ordinary concrete.
From M20 to M60, they are known as standard concrete.
M65, M65 and upto M100 are known as high performance concrete.
As per IS 456-2000 the M20 is the minimum grade of concrete for RCC.
A lot factors affect the final strength of concrete.
Some are - Mix Design
-Curing
-Grade of cement etc.
You can find more at Grade of concrete in details.