The title of your question seems to clearly indicate reflexive verbs, while the body of your text simply refers to intransitivity.
To your explicitly stated question, a verb for which the subject and object are implicitly the same is reflexive (at least that is how it would be classed in other languages which show relevant verb morphology). You can think of these as situations in which you could add a reflexive pronoun:
A) She washed before dinner.
B) She washed (herself) before dinner.
BUT this would not apply in the specific example you have chosen above, because while it is possible to say "the battleship sank itself" no one in their right mind would assume this- it would be assumed that the battleship sank due to circumstances outside its control, rather than that it might be the agent in that situation.
Also it is important to remember that both reflexivity and transitivity are unfixed (especially in English), which means that these properties are not inherent to the verbs (per se).
We can take a verb like "wash," insert a DO, and it is no longer reflexive:
C) She washed (the dishes) before dinner.
Likewise we can take a verb like "give," which is traditionally a two-place transitive verb (meaning it requires both a direct object and an indirect object), and make it intransitive.
D) All she ever did was give.
I will also note that since verbs in English do not show any morphology to indicate reflexivity, these situations should maybe be thought of as special cases of intransitivity, rather than as a separate verb category.