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Logically they're the same, but electrically they're different. Using twice the components to make up the same socket density requires extra power & can have other effects. It usually works but results can vary. Sometimes motherboards aren't designed to supply the power required or a mismatch can cause detection issues.
The different styles result from component cost and availability. If you're a DIMM manufacturer/assembler and have a cheap source of 128Mbit chips, it can make economic sense to use twice as many instead of sourcing expensive 256Mbit chips. This has been a classic pattern when a new chip capacity is released but commands a premium price. For obvious reasons it's been most common with "budget" suppliers.
Again, the jumbo modules are usually okay but can cause issues. No foolproof guideline but problems usually only arise when mixing types or when used in a board that wasn't tested for the added load.
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