The GT730 is a perfect example. There were several versions and care must be taken to see which one you were purchasing.
- 700MHz, DDR3, 2Gb, 128bit bus, 96 Cuda cores
- 902MHz, DDR3, 2Gb, 64bit bus, 384 Cuda cores
- 902MHz, GDDR5, 1Gb, 64bit bus, 384 Cuda cores.
- was best used for video watching, htpc etc
- A Dog, the DDR3 and 64bit bus killed any performance in graphics and video.
- was best used as entry level gaming. Lightweight games didn't require lots of ram, just higher performance ram and the cores to handle it.
Game files realistically are tiny, from several Kb to a couple of Mb, so getting them pushed through the ram faster meant less reliance on amount of ram.
Same thought process applies to modern cards, someone using a gpu to render will be better off with 8Gb of GDDR6, but someone gaming would be better off with 6Gb of GDDR6x. If the game didn't max out the available ram.
There's multiple factors in a gpu, cores, clocks, boost clocks, effective speed, ram type, ram amounts, memory clocks, bandwidths, power limits, usage etc, so memory type or memory amount is just 2 factors out of many. A 4Gb card may perform no different to a similar 2Gb version, with the same ram speeds, may even perform worse depending on usage and other factors.