What are the similarities between capitalism and socialism?
One similarity between capitalism and socialism is that both systems consider labor and capital to be the primary economic forces. Both capitalism and socialism agree that the world is composed of a variety of natural resources that are for the most part value-neutral until human labor imparts value to them. In this way, both systems are labor-centric. Capitalists believe market competition should direct the distribution of labor; socialists believe the government should have that power.
Additionally, both capitalism and socialism recognize capital (or wealth) as the rubric against which one should measure the economy. Capitalists believe that private ownership of capital produces the most economic growth; socialists believe the government should control the allocation of capital to promote the greater good of the entire economy, not just the wealthy.
Different people might see different similarities between these systems, depending on the exact definitions that they are using. I suggest that you consult your textbook and/or your class notes to see what answer your instructor expects to see.
In my view, a major similarity of these two systems is democracy. While democracy is not absolutely essential to either of these systems, it is the most common form of government in capitalist countries and even in socialist (as opposed to communist) countries.
With regards to economics, the main similarity between the two, as I see it, is some amount of market competition. A purely capitalist economy (no country has such an economy) would be run completely by market forces. The government would not intervene in the economy at all. A socialist system would be under more government control than a capitalist economy, but there would still be many market forces at work. People would be able to own private property and make many of their own economic decisions. Small-scale private enterprises would be allowed to exist. Thus, both systems would include market forces, though such forces would play a larger role in a capitalist system.
Democracy and market forces, then, are the main similarities between these two economic systems.