Ukraine demands that they are to be treated as prisoners of war, which according to the Geneva Convention implies that their public display is unlawful.
Russia insists that since no official state of war has been declared between both countries, the event is treated as a regular, unauthorized border crossing and the arrested men are prosecuted as criminals.
Both Russia and Ukraine (as Soviet Union) have signed the Geneva Convention. This includes Part III (Convention (III) relative to the Treatment of Prisoners of War), which also states that the protection for POWs needs to be guaranteed even if the war is not recognized as such by one of the parties involved:
Convention (III) relative to the Treatment of Prisoners of War. Geneva, 12 August 1949, Article 2:
In addition to the provisions which shall be implemented in peace time, the present Convention shall apply to all cases of declared war or of any other armed conflict which may arise between two or more of the High Contracting Parties, even if the state of war is not recognized by one of them. The Convention shall also apply to all cases of partial or total occupation of the territory of a High Contracting Party, even if the said occupation meets with no armed resistance.
Undoubtedly there is an armed conflict going on, in who's context the arrest needs to be viewed. Ukraine makes it clear that they consider the conflict an armed invasion by Russia and not just a regional, internal conflict. However, a war between both countries has not been declared officially by either side. Russia refuses responsibility or influence with regards to the conflict and says any actions of separatists are not related to or supported by the government/military.
This incident is noticeable because it marks the first time the Russian military has acted also officially in the Ukraine war, as mentioned in the answer to this question. As such it qualifies as an armed conflict between two signatories of the Geneva Convention, in particular the sections concerning POWs.
Under these circumstances in which both countries haven't issued a declaration of war, does Russia need to treat the sailors as POWs or is Russia's behavior in their prosecution 'ok' according to commonly accepted standards/laws?