Predicate nouns and adjectives both follow linking verbs in sentences and rename or describe the subject. The difference between linking and action verbs in a sentence is that an action verb shows the subject either doing something (in active voice) or having something done to it (in passive voice). The roles of the predicate noun and adjective are very similar.
Predicate nouns rename the subject in the sentence and follow a linking verb. Linking verbs include all the forms of "to be," all the synonyms of those verbs (such as appear or seem), and the sense verbs (sounds, smells, looks, feels, tastes).
For example, if you say, "Howie Mandel was the first host of 'Deal or No Deal,'" the linking verb is "was." "Howie Mandel" is the subject, and "host" is the predicate noun renaming Howie.
Predicate adjectives describe the subject and follow a linking verb.
For example, if you say, "Dinner will be excellent tonight," "be" is the linking verb. "Dinner" is the subject, and the predicate adjective describing it is "excellent."
With sense verbs, it would look like this, "That new band sounds amazing!" "Band" is the subject, "sounds" is the linking verb, and "amazing" is the predicate adjective.
You can run into trouble, especially with the sense verbs, if you don't pay attention to the function of the verb.
For example, in the sentence, "The dog smells terrible," "smells" is a linking verb, because there is no action in the sentence. However, "The dog smells the cat behind the door" indicates an action. "Cat" is not a predicate noun; instead, it's the direct object, because it's what the dog smells.
When you're diagramming a sentence, you would use a vertical line that stops at the main horizontal line to separate the action verb from the direct object. For both the predicate noun and adjective, you use a line that tilts back toward the subject to separate the verb from the noun or adjective, to indicate that it renames or describes the subject.