What is the difference between the columns PID and SPID in v$process?

The PID column is an internal counter that oracle uses for its own processes. It is incremented by one for every new process. Consequently, since every session creates its own server process (also called "shadow process") you will see the number increment by one for each session that connects.

The documentation for V$PROCESSES states that PID is the "Oracle Process Identifier" which is confusing.
In most circumstances, the column that you would need is the SPID, which shows the "Operating system process identifier".