I've noticed when I reconnect to internet, the last two bytes of IP address static IP changes.
Does that mean when I disconnect someone else could have the same IP? How does this process differ from dynamic IP?
If your IP address is changing, you don't have a static IP address, but a dynamic one, and thus your answer is that "this process" does not differ at all from dynamic IP assignment because it is dynamic IP assignment.
And yes, it does mean that when you disconnect, someone else could get "your" IP address dynamically assigned to them when they connect.
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It is usually done the same way your home router does it, but with much more expensive equipment. It is more expensive because it is far more configurable. The ISP I work for uses an ERX to serve IPs, it stores mac addresses in its arp table and assigns ip address based on the card and port, which is mapped to a circuit through ATMs and eventually a DSLAM (or CMTS on similarly setup cable providers) - we statically assign, but not based on DHCP. This is the case with both bridged and routed circuits, where routed circuit simply have blocks on static routes over a /32 wan.
Other ISPs will use the arp table to assign addressing via DHCP, where static address are simply removed from the DHCP pool, but will appear on the lease table. This static is also usually mapped to a port and card on the router so you can only get it on your own circuit (but not always). In cases where you have a dynamic address, if your lease runs out and your device is not connected to renew, it will be handed out elsewhere and you will get the next available in the pool when you reconnect. Some leases last a few hours, some up to a week, depending on your ISP.
There are of course other configurations, but these cover the most commonly seen.
EDIT: I forgot to add, most single ips are /32 and are divided from a larger block. These blocks are usually assigned by region (or ISP in the case of smaller ones) which is why all IPs that you get will be very similar except for the last octet (or last two in the case of larger ISPs.