Private property and personal property are different, at least in most schools of economic thought. Personal property is items directly owned and used by a person or family, things like the house they live in, their car, tools they use on the regular, the clothes they wear.

Whereas private property is items which are considered owned by a entity, but that entity may not directly be using them (although they usually are profiting from them). A landlord would own a bunch of rental houses, all of which are their private property, a business owns a factory which is it’s private property. Stockholders own stock, private property.

When certain leftist groups talk about abolishing private property they are much more talking about it in the above sense. Usually no one is advocating abolishing personal property, but certain economic systems see private property as the root of a lot of societal ills. The thought being that unless your directly making it or working on it you have no real right towards it. Then again many economic systems see the invention of private property as the most important thing for the advancement of our civilization, saying it allowed for the flexibility of trade which led to planning and eventually everything, so opinions are abundant.