Think of it like the access to a publicly listed company vs a private one.
The main difference between public and private blockchain is related to who is allowed to participate in the network, execute the consensus protocol and maintain the shared ledger. A public blockchain network is completely open and anyone can join and participate in the network. The network typically has an incentivising mechanism to encourage more participants to join the network. Bitcoin is one of the largest public blockchain networks today.
A private blockchain network requires an invitation and must be validated by either the network starter, or by a set of rules established by the network starter. Businesses who set up a private blockchain, will generally set up a Permissioned Network. This places restrictions on who is allowed to participate in the network, and only in certain transactions. Participants need to obtain an invitation or permission to join.