I know there is the Lysmata wurdemanni, which comes from the the Atlantic and the Gulf of mexico. This is what I want and the most common.
You are mostly correct, however, there is more information to digest. I've been posting about this for years but most seem not to comprehend......
The original Aptasia eating shrimp of marine aquarium lore is
Lysmata wurdemanni*.
However, the species which is most commonly sold TODAY as "peppermint shrimp" is Lysmata rathbunae*.
Also, there are at least 2 other local species that can occasionally appear in traps as well. Add in the possible hybrids of the 4, coupled with a reclassification of the local species in 2006* and identification is a real joy.
Even though the species are similar with geographical ranges and habitat that overlaps their behavior is different, which explains the hit or miss success and horror stories hobbyist experience. From experience, no matter the actual name, the only consistent Aptasia eating shrimp which rarely if ever molested desirable tank inhabitants was the critter formally known as
Lysmata wurdemanni*, first picture. Unfortunately, in their native habitat this species appears to have been displaced by
L. rathbunae*. "Rathunae" is now the bulk of the critters being offered as "Peppermint Shrimp".
*=
A WESTERN ATLANTIC PEPPERMINT SHRIMP COMPLEX: REDESCRIPTION OF LYSMATA WURDEMANNI, DESCRIPTION OF FOUR NEW SPECIES, AND REMARKS ON LYSMATA RATHBUNAE by Andrew L. Rhyne and Junda Lin
Despite what anyone may promote, I believe the original miracle shrimp "Wurdemanni" is long gone from the hobby. It appears "Rathunae" has massively displaced "Wurdemanni" in local waters. IMO, the "myth" is perpetuated due to the huge economic incentive to continue selling "Peppermint" Shrimp.
Then again, what the heck do I know being "closed minded" and all.