"Jar" must be vernacular, never heard it on the left coast.'Jar' is the street term for a lead-acid flooded cell battery...
Not sure how old batteries killed your starter on your Powerstroke and I've replaced the starter on my 1997 and a new reman one was 120 bucks.
I have Interstates in my 1997 and when parked it's always on the battery tender.
In my case I was forced to go to a Ford dealer that opened at 7 AM (I just got off work, had AAA jury rig a jump start), and had a NEW (reman n/a) $550 starter installed for $350 labor. Working a 12 hour shift didn't give me enough time to do the job myself and still get some sleep before work again. I was over a barrel with no lube!