Pure capitalism can be seen in the US. Businesses are run using capital. Those with the capital have a better edge in running the market. Capital investments, shares, labor, and industries are capital based. The economy gets interconnected with capital. Thus, this makes the US a good capitalist model. However, in this design improvements and profits are not equalized but heavily competed.
On the other hand in socialism, industries are all nationalized or operated by the government. The concern of this economic system is to equally divide the wealth among the people. Everything is centered on the government to control.