AM requires a ground plane, but not FM. You only need to ground it for power of amplifier if using for FM.
One I have is ground thru antenna connector, Plus I grounded to frame inside console for ground plane and tied ground from battery and radio to same framing. Did this more to eliminate noise and any ground loop that may occur.
If you notice any home FM radio you purchase you get just piece of wire for FM. One could make you own FM antenna easy with piece of wire, Thing that is most important on FM antenna is length of unshielded wire. Different lengths can be made to optimize reception of station you are looking for most.
I used to build and car audio switcher displays for local chain store. I built my own antennas for them, tuned to higher end of radio band due to most of our stations in area were in that freq. band. We now build for our home theater and multiroom sound systems in basements due to the poor reception below ground level. We run RG-6 into attic area and strip braided ground off , so cooper is exposed to appropriate length. One could do this for boat but if tin boat would need to have wire above metal for best reception. If had fiberglass boat one could fish around front of bow and have no issues.
The small black one you were referring to would be shorter antenna and considered 1/4 wave antenna. Best reception would be first one Palmer812 posted extended out all the way. I did no use that because I did not want to drill another hole in my boat, plus have a mast to have to fish around.
Here are directions on building antenna from how to site:
Calculate the proper length for your antenna according to where your favorite stations are on the dial. Public radio stations are usually located from 88 Mhz to 92 Mhz. The best length for a quarter wave antenna would be 26 inches. A half wave antenna wire would be 53 inches.
Remember these antenna lengths are approximates. There are many web sites where you will find the mathematical formulas for precise measurements. Listeners who have more than one preferred station may choose to use one of the following lengths. For a quarter wave antenna on the low end of the dial, 26 inches; mid dial, 29 inches; and upper dial, 33 inches.
Cut your antenna for the mid dial position to give you reasonably good reception for stations above and below the mid point and is in most cases the best overall choice.