Let's look at oniya first. It means "ship", and appears 31 times in the Bible. The related word oni אני, meaning a fleet of oniyot, appears seven times. Klein says that oniya dervies from oni, and both come from a root אנה, which in a number of Semitic languages means "vessel". He points out that in other languages as well, such as English, the word vessel means both "container" and "ship".
Sefina, however, appears only once in the Tanach - Yona 1:5. Despite the explanation by many that sefina and oniya are synonymous, the fact that both words appear in that verse seems to belie that argument:
וַיִּירְאוּ הַמַּלָּחִים וַיִּזְעֲקוּ אִישׁ אֶל-אֱלֹהָיו וַיָּטִלוּ אֶת-הַכֵּלִים אֲשֶׁר בָּאֳנִיָּה אֶל-הַיָּם לְהָקֵל מֵעֲלֵיהֶם וְיוֹנָה יָרַד אֶל-יַרְכְּתֵי הַסְּפִינָה וַיִּשְׁכַּב וַיֵּרָדַם.
In their fright, the sailors cried out, each to his own god; and they flung the cargo of the oniya overboard to make it lighter for them. Yona, meanwhile, had gone down into the hold of the sefina where he lay down and fell asleep.
This site explains the difference between the terms in the verse:
The noun סְפִינָה (sÿfinah) refers to a “ship” with a deck (HALOT 764 s.v. סְפִינָה). The term is a hapax legomenon in Hebrew and is probably an Aramaic loanword. The term is used frequently in the related Semitic languages to refer to ships with multiple decks. Here the term probably functions as a synecdoche of whole for the part, referring to the “lower deck” rather than to the ship as a whole (R. S. Hess, NIDOTTE 3:282). An outdated approach related the noun to the verb סָפַן (safan, “to cover”) and suggested that סְפִינָה describes a ship covered with sheathing (BDB 706 s.v. סְפִינָה).
The "outdated" approach is the one suggested by Klein, who writes that it "probably derives from ספן (= to cover, panel) and literally mean "covered, overlaid, with deck".)
Sira also appears only once - in Amos 4:2. There are those that explain it to mean there as "small fishing boats", but most say this is a misreading of the verse (see Daat Mikra), and it should be instead understood as "hook" or "thorn". Ben Yehuda does not even include the meaning of boat in his dictionary, but proper understanding of the verse or not - this is the only meaning still used in Modern Hebrew.
In Mishnaic Hebrew, we find almost exclusive use of the word sefina for ship. Based on this, Joseph Klausner wrote that Modern Hebrew should adopt sfina instead of oniya, for it is the later (i.e. more recent) term. This was a constant battle for Klausner - which he generally lost, as Biblical Hebrew was usually preferred over Mishnaic. In this case, though, both words were used, with the distinction being that an oniya was larger than a sefina (similar to "ship" vs "boat"). Klausner seems particularly frustrated that oniya is used in Modern Hebrew, when sefina is a much "richer" word for creating related forms like סיפון sipun - "deck" (originally "ceiling" - see Melachim I 6:15), ספן sapan - "sailor", and מספנה mispana - "dock".
But as we pointed out earlier, oniya and sefina were clearly not synonymous (see also this article), so it makes sense that Modern Hebrew would distinguish their uses. And in fact, the meanings are even established by law:
oniya - a vessel, powered by a motor, whose maximal length is at least 24 meters
sefina - a vessel that is not an oniya, whose maximal length is between 7 and 24 meters
sira - a vessel that is not an oniya or sefina, with a length of up to 7 meters
So I don't know if this will make it easier to understand the events in the news, but at least we can all know the difference between the terms...