The 'shielded' ones are usually the Espressif-made
"modules", and when they are, they have an FCC EMC certification. The unshielded ones are usually not FCC or otherwise EMC certified and hence may in theory not be legally operated, much less sold when built into a product, in many jurisdictions, or only operated if you have a HAM license.
Plus, the bigger dev board also has a USB<->UART converter on board (for an extra/dedicated UART connection), and an RGB LED.
Functionally they're identical, but different chips and modules come with different sizes of flash memory and (optionally) external PSRAM.
How much flash you should buy depends, of course, on the application(s) you have in mind. Note though that, if you want "over-the-air" (OTA) firmware updates, you'll need at least 2x the application size of flash (one application "partition" is running while the other one is being updated/overwritten by the running application). 4MB of flash is the low end, and may not be enough for a 'reasonably' sized application with OTA capability.
"External"/PSRAM is needed for some use cases, e.g. if you need to framebuffer a big-ish TFT display or some kinds of real-time audio processing. Notice that the internal SRAM is "only" half a MB, of which 1/4 to 1/3 is easily taken up by application/OS code copied to RAM. Add the network stack and a handful of concurrent TCP connections, and 1/2 or more of the internal RAM may be used up before your application can even do anything useful. TL;DR: Having 4 or 8 MB of "external" RAM is quite beneficial for many applications on the ESP32-S3. Only downsides of having it are 1) slightly higher cost, 2) potentially higher power consumption in sleep mode, 3) one less IO pin available for other things.
(I put "external" in quotation marks above because nowadays chips can be had which house that "external" PSRAM in the same plastic package as the rest of the MCU; logically and electrically it's still "external" to the MCU though.)