Find the list that best matches reference list

MaximalBy[Length[a⋂#]&]@{b,c} 

{{"S280", "G281", "I282", "I284"}}

MinimalBy[Length@Complement[a,#]&]@{b,c} 

{{"S280", "G281", "I282", "I284"}}

Maybe:

LongestCommonSequence[a, b]

{"S280", "G281", "I282", "I284"}

LongestCommonSequence[a, c]

{"A278", "G279"}

Length@LongestCommonSequence[a, #] & /@ {b, c}

{4, 2}

Suppose I have the reference list a and a matrix otherLists of all other lists I want to compare against a:

otherLists[[Ordering[Length[#] & /@ (Complement[a, #] & /@ otherLists), 1]]]

This will return the list that best matches a.