Personally I think 'explore' as a mode is misleading when it's more like a 'free roam'. Explore covers the same areas as the story mode, just with mini quests such as scout here, or kill these things, with reputation as the payout. Also good for bounties.
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Just to add there are chances of running into random public events such as a Devil Walker being dropped into the 'room' (one common instance in the beta), and anyone in the area can engage it.