When we talk about public IP, we are actually talking about public IP address
(as opposed to private IP address).
Concretely, the public IP address of your home corresponds to your IP address visible from the Internet. It is this address that allows websites/companies to uniquely identify you on the Internet.
An IP address generally corresponds to an identifier on an IT network. This address can therefore be used to identify a machine (computer, modem, telephone, adsl box...) connected to this network.
The concepts of "private" and "public" distinguish the type of network
A private network is not accessible from the Internet (by example, your computer network behind your Internet box or your router), and the addresses found on this network can be present on several private networks.
The public network is Internet. It is not possible to find several machines with the same IP address.
Static and dynamic IP addresses
A static IP is an IP address that does not change. A dynamic IP
is an IP address that will be renewed each time
you connect to a network, or periodically after a period of time
On the Internet, some ISPs provide static IPs for individuals, but most of them work with a dynamic IP system (new IP address at each time you reconnect to the network/reboot box).
Most boxes also provide dynamic IPs for your private network.
A hostname is a name associated with an IP address. This name makes it easier to identify a machine on a network (public or private), unlike IP addresses, less easy to remember. The correspondence between host name and IP address are usually provided by DNS servers.
It is a server that allows making the translation between hostnames and IP addresses. When you browse the Internet, you will pass without knowing it by a DNS server so that your computer can determine the IP address to access a website.
We often talk about a Reverse DNS request. It is in fact a question of a request sent to the DNS servers to find out the hostname from an IP address.
Geolocation makes it possible to determine the location of a public IP address. The data are relatively reliable for fixed IP addresses, but more random for dynamic IPs.