SLSA = Special Light Sport Aircraft. This is one built not to FAA standards but to consensus standards developed by light sport aircraft manufactures and administrated by a private organization rather than a government one
as opposed to
ELSA = Experimental Light Sport Aircraft, an aircraft such as a "heavy" ultralight or a two seat ultralight (whither manufactured or homebuilt) that meets the light sport aircraft specifications and is registered as a LSA
as opposed to
Experimental/homebuilt aircraft that meet the light sport aircraft specifications but are not registered as a LSA.
as opposed to
Certified aircraft that were built by manufacturers that met the FAA certification standards and the aircraft happens to meet the light sport aircraft specifications.
All of the above can be flown by a pilot with a light sport pilot license.
Main limitations of light sport pilot license:
no night flying
no flying above 10,000 ft
no flying into towered airports without sign-off by CFI provided the plane is properly equipped
A pilot with PPL can fly a suitably equipped Light Sport Aircraft at night, above 10,000 feet, and into towered airports, and even under IFR.
Main limitations of a plane that meets the light sport plane specifications:
must have no more than two seats
a max gross of 1320 pounds or less
a max cruise speed of 130 miles per hour
a max stall speed of about 52 mph (45 knots exactly)
Note: almost every statement above has one or more exceptions (of course).