There are different PvP-situateions you might have been a part in:
-- Player attacking a player’s planet.
-- Player attacking a player’s resource wrecks.
-- Player attacking space structures (under development).
-- Player defending on planet against player’s attack.
-- Player defending on wrecks against player’s attack.
-- Player reinforcing a corpmate against player’s attack.
-- Player defending space structures (under development)

The most noticeable difference between PvP and PvE, is regarding minimum flight times and lost ships.

While on PvE the minimum flight time to target is 3 seconds, on PvP this is increased to 30 seconds. This means that, no matter how close you are to the target, or how fast your ships are, there will always be AT LEAST 30 second flight time to the target.