Is a Light Sport aircraft considered to be A certified or experimental aircraft? or is Light Sport a completely different third category?
Light Sport is not Experimental, (which includes amateur homebuilt aircraft, warbirds, etc.) it is a category of its own within the broader group of Certified aircraft.
So it's not really a "completely different third category", but more of a different set of standards that exists within Certified.
You are commingling certification and category. All aircraft in the US are certified by the FAA (the FAA does not consider Ultralights to be aircraft). LSA, a category of small aircraft defined by the FAA using criteria such as maximum weight, number of seats, etc., are certified by the FAA under FAR 21.190 https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-21/subpart-H/section-21.190, as are Experimental aircraft https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-21/subpart-H/section-21.191. Experimental airworthiness certifications are issued irrespective of aircraft category, weight, number of seats, etc. I’m assuming you mean operating Experimental- Amateur Built aircraft when you state “experimental” as there are several other purposes experimental certifications are issued. A way to differentiate the certification process between Light Sport and Experimental is the FAA approval requirement for the aircraft manufacturer’s data, and the aircraft owner’s responsibility to adhere to the approved data. For example, for the LSA manufacturer to obtain a certification, the FAA must approve the LSA manufacturer’s Pilot Operating Handbook and Maintenance Procedures. The person that buys and/or pilots that aircraft must operate the aircraft in compliance with the approved data and may not arbitrarily substitute parts, alter, or repair a component without using the original manufacturer’s approved data. These restrictions are not required of the manufacturer or any owner/operator of an aircraft certified as Experimental Amateur Built.