Whether it’s in a desktop or laptop, computer memory typically comes on a 64-bit module. That module typically has two 64-bit interfaces, one on each side. The term DIMM (Dual Inline Memory Module) references these two interfaces, which are addressed in series, so that a module that has memory on both sides is addressed by the memory controller in the same manner as two single-sided modules. And in days past, builders would refer to these as single or double-sided.
Yet it’s not always necessary to put ICs (chips) on both sides of a module to access both interfaces: Some companies found it cheaper to put twice as many chips on one side and use soldered-through holes (called Vias) to connect half of the ICs to the opposite side. That left users confused as their single-sided modules addressed both interfaces, so they started calling them “Banks”. Again there were problems as that term was being used differently within the memory industry, which is why the official term Ranks entered the common vernacular.
The impact of whether a module has one rank or two isn’t merely semantic, as memory controllers may have different frequency limits as more ICs are addressed. And most of the memory controllers integrated into consumer CPUs can only address up to four ranks per channel, which is why so many motherboards have two DIMM slots per memory channel. Further, a technique called “interleaving” allows internal operations (such as opening and closing columns and rows) to occur on one rank while data transfers on the other, thereby reducing the number of unused transfer cycles during the brief period that data is being retrieved within a rank (called latency).
So the difference between single and double rank DIMMs are that the latter can have twice the capacity (twice as many ICs), less latency during certain operations, and may limit the memory controllers of certain CPUs to a lower stable frequency.