Conjunction is a part of speech used to connect words, phrases, or clauses. A linking verb is a verb (usually a BE-verb) used to connect the subject to its predicate nominative/adjective.
Conjunction used to connect words: Michael and Stephen are joining the contest.And connects “Michael” and Stephen”.
Conjunction used to connect phrases: The children were running around and making so much noise.And connects “running around” and “making so much noise”.
Conjunction used to connect clauses:Either Marie will take summer classes or her father will send her to the province.Either … or connects “Marie will take summer classes” and “her father will send her to the province”.
Linking verb joining subject to predicate nominative: Mr. Castro is the new president of the company.Is connects “Mr. Castro” and “president”.
Linking verb joining subject to predicate adjective: Carol is very talented.Is connects “Carol” and “talented”.
Mom’s cake smells delicious.Smells connects “cake” and “delicious”.
Note: Not all linking are BE-verbs as in the case of the word “smells”.