Both capitalism and socialism are spectrums of systems rather than single monoliths so any definition is going to be fuzzy. However, it's probably useful to specifically say that in capitalism specifically private property and/or capital can be owned. Generally speaking, socialist systems still allow personal property to be owned, they just place restrictions on the ownership or private property and/or capital.

It's also probably worth considering that socialism doesn't necessarily have to forbid ownership of private property or capital outright. It could, for example, mean that revenue/profit/income derived from private property or capital is taxed more highly than revenue/profit/income derived from labor.