In addition to what others have said, the boundaries between these can change according to the society and time. Fifty years ago, a computer would have been 'private property'. Nowadays most computers are 'personal'.

Whether you can own a house or a couple of acres under a hypothetical socialist system would mainly depend on population density. The Soviets used to give young people large tracts of land in rural areas because land isn't really a scarce resource in Russia. (Vietnam still does this, but the plots are smaller.) On the other hand, Singapore, a capitalist country, has no private land ownership because land is so scarce.