There can be different responses to your question, depending on which definition from the Oxford dictionary you go with.
Based on the first definition:
"The practice or principle of giving a group priority over each individual in it".
"Collectivism" isn't synonymous with "Communism" or "Socialism" nor is it antynomous with "Capitalism" - all of which are economic systems. On the other hand "Collectivism" would be a stance on human rights, ethics and social norms, and should be contrasted with "Libertarianism" or with "Individualism", not with the above mentioned economic systems.
From this point of view both Soviet style communism, and excessive forms of capitalism where large corporate interest impose lifestyle and economic choices on hapless individuals are both collectivist - whether the entity doing the coercion is a government actor or a private corporate interest doesn't really matter.
In fact many leftists and socialist thinkers saw themselves as opposing the collectivism imposed by capitalism.
Marx for example saw the division of labor as a limitation of freedom imposed by the capitalist mode of production: Capitalism force people to be either doctors, or bus drivers, or coal miners, or musicians, etc...whereas in a communist society people would be free to engage in whichever activities they please. In the The German Ideology (1845) he states that:
...while in communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticise after dinner, just as I have a mind, without ever becoming hunter, fisherman, herdsman or critic.
Similarly Adorno and Horkheimer, in The Culture Industry saw Capitalism as imposing a unified artistic aesthetic on society, a factory produced bland art that is used to deceive the masses, while legitimate "high" art needs to be free and creative to satisfy human psychological needs.
I have also heard of capitalists who argued that collectivism is a good thing, but then went on a step further by claiming that capitalism is better at achieving collectivism than socialism is, by allowing any individuals to purchase shares in corporations through the stock market, and through things such as employee stock ownership plans. I don't remember the reference for this, but it might have been mentioned in this interview with Herbert Marcuse.
So the direct answer to your question is: Based on the first definition, there is no distinction between collectivism as it applies to communism or to capitalism. Whether collectivism is good or bad, it can be the result of both communism/socialism and of capitalism.
Based on the second definition:
"The ownership of land and the means of production by the people or the state, as a political principle or system".
Based on this definition, it seems that superficially that both communism and capitalism where the rights of large corporations take precedence of the rights of individuals amount to forms of collectivism.
A libertarian defender of (free-market) Capitalism, such as Robert Nozick or Ayn Rand, can argue that nonetheless, Capitalism does preserve individual freedom where socialism/communism don't in the following way:
- In communist and socialist systems the workers don't have any choices. They are constantly coerced by the government and by restrictive labor laws and union rules (For example in many socialist countries, you are not allowed to just resign from your job, you have to have give several months notice, and your management has to approve your departure). In a capitalist system on the other hand, the worker is free at any time to leave the company if he doesn't like conditions he is working in (Of course he will likely starve to death, but he is doing so of his own free will).
- In communist and socialist systems, the will of the individual is sacrificed to the "greater good". In capitalist systems, individual workers are sacrificed for the good of the shareholders who also happen to be themselves individuals, i.e. capitalism does focus on individual rights, it's just that is focused on the individual rights of shareholders not the individual rights of workers, and as mentioned above those workers freely entered into contractual agreements with their employers, nobody ever forced them into anything.
So the libertarian will argue that the capitalist system is not collectivist insofar as it protects individual ownership and property rights, which are the only rights that really matter.