In a categorical syllogism, the conclusion follows from the premises through a valid form, provided the relevant conditions are met. Analogy proposes transferring a judgment through a claimed shared cause.
Analogy: This copper rod conducts electricity; the second rod is also copper; therefore we expect it to conduct.
Syllogism: Every pure copper rod conducts under suitable conditions; this rod is pure copper; therefore it conducts under those conditions.
The second inference explicitly contains a universal premise. The first must establish the general relevance of the shared property.