Is "flash storage" the same "SSD"? I'm looking to see if the two are interchangeable and if not what the differences are. 

If the two in fact have a difference, perhaps adding devices or cases where each are normally used over the other.
Yes and no.

Flash storage is storage that uses electronically programmable and erasable memory modules with no moving parts. It refers to a very specific implementation of data storage. It can come in different packages though: wrapped in a hard, plastic envelope you slide in to your camera; mounted to a PCB stick with exposed connectors and docked inside your MacPro; or mounted inside a drive enclosure that's slid in to an existing drive bay.

SSD, or Solid State Drive, refers to an enclosed storage device that's meant to act as a disk for a computer, but is lean on details about what's inside the enclosure and being used to store the data.

Technically, "solid state" just refers to "electronics with no moving parts". So a "solid state drive" that used ferromagnetic fluids to store data is still an SSD.

And indeed, SSDs have been around for a long time with a variety of different solid state storage mediums inside of them to keep those 1's and 0's persistent. However, in this day and age, at the time I'm writing this, SSDs are generally filled with (you guessed it): flash-type memory modules. Though flash-based SSDs generally carry the property that their enclosure is built to mirror that of a typical 2.5" spinning drive disk enclosure with an SATA interface so that it can act as a drop-in replacement for a mechanical disk.