Most nonbasic lands don’t have basic land types, even if they produce colored mana. For example, Caves of Koilos is neither a Plains nor a Swamp. Having one enter the battlefield under your control won’t cause Staff of the Sun Magus’s ability to trigger.

If you cast a copy of a card that’s a certain color, the appropriate Staff’s ability will trigger. However, if you copy a spell on the stack without casting that copy, it will not.

Each of these artifacts cares about any land with the appropriate basic land type. For example, Staff of the Sun Magus’s ability triggers when any land with the subtype Plains enters the battlefield under your control, not just lands named Plains.