A few things, not to be a stick in the mud.
Now, there are a few classification systems in use, but generally speaking, sea slugs, snails, squid, etc. all belong to the phylum Mollusca. The snails and slugs are further divided into the class Gastropoda, and the majority of seaslugs into the subclass Opisthobranchia. Then, depending on who is doing the classification, the subclass is divided into various orders, including Anaspidea (sea hares), Saccoglossa (sap-sucking slugs), and Nudibranchia (the nudibranchs.)
So "sea slug" can be used as a general term for Opisthobranchs, but "nudibranch" should really only be used for those slugs who are in the order Nudibranchia.
The "lettuce slugs" are in the order Saccoglossa.
The one in TampaBayReefer's link is identified incorrectly. First, an old genus name is used. The correct genus name is "Elysia." Second, that most likely isn't the correct species name, either, by the color on the rhinophores. Rather than a Western Atlantic species, it is likely the Pacific species E. diomedea. I am not aware of any scientific food studies on E. diomedea.
There is no scientific evidence that Elysia sp. will eat any green hair algae; studies done with some of the species from the Western Atlantic did show that these species could survive on Bryopsis alone, although Bryopsis is typically a food only for the younger slugs.
Oh, and no, these slugs will not "nuke" a tank when they die, unless you do not have the capacity to take up the extra bioload of the animal's decay.