What is the difference between pure capitalism and modified capitalism?

Free-market capitalism is based on free markets, private ownership of the means of production, and limited regulations and some government provided goods and services.

Mixed capitalism has more heavily regulated markets, mainly private ownership of the means of production but also features a greater role for state-owned enterprises, and usually has economic intervention in markets to correct market failures.

Both are similar in that they are both based on the process of capital accumulation, both systems attempt to maximize private profits, and both are mainly privately-owned.