BTW I noticed they’ve dropped the JMSDF in favor of JS. More evidence Japan is finally entering the post-post war era.
Two different animals. JMSDF refers to the organization itself, like USN. JS (Japanese Ship) is analogous to USS or HMS in a ship's name. I see this is now the usage on US Navy web sites but JMSDF official websites in English simply refer to ships by type (minesweeper Chichijima, escort vessel Teruzuki, etc.)
When this changed I don't know, but I have a ball cap I got in 2006 on my last deployment from the oiler Tokiwa that says "JDS TOKIWA AOE 423", the JDS being Japanese Defense Ship.