Well historically a pvp server is a pve server that allows pvp anywhere. Any zone any place you can pvp in.
Take wow for instance, the pvp server I played on Sargeras. If we had a Horde come into the dorf home city everyone in that city could attack him. If we were outside the city you could attack.
The major draw back for a straight pvp server is that when you want to pve and do your quests you have to watch over your back, you can be camped and harrassed by higher lvl players or well by anyone who wants to harass you.
it can be a major drag if your traveling a great distance and havent like updated your spawning spot and then you die, only to end back hundreds of thousands of miles away from your body.
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