Your sentences are cases of "syntactic ambiguities," i.e. they can be parsed (analyzed) in more than one way. All cases of this kind of ambiguity can be solved by adding context, but let's see what grammar has to say.
- They can fish
In this sentence the ambiguity results from whether you will take "can" as a modal auxiliary modifying the verb "fish" or as the regular, transitive verb "can" in the Simple Present with the noun "fish" as its direct object. These might be paraphrased as the formal "They might fish" and "They know how to fish."
- Terry finally decided on the boat
In this case, the ambiguity lies in the connection between "decided" and "on the boat." You have semantic ambiguity as well, since "to decide on s/th" [decide on something] means "to choose one particular object rather than another." If you parse "on the boat" as an adverbial phrase of place, "decided" refers to a decision about something excluded from the sentence. This decision was made "on the boat." On the other hand, if your internal bracketing of the sentence is [...] (decided on) + (the boat), "decided on" is analyzed as a transitive prepositional verb whose direct object is "the boat."