All hail the mighty alternator and its nearly instant battery charging proclivities.
Or so it seems.
After a jumpstart is required, relying solely on the alternator for a full recharge the jumped battery is unwise in the extreme. The last 20% will take hours and hours no matter what the charging source is. Returning the battery back to 80% might not take all that long depending on the vehicle's capabilities and actual remaining capacity in the battery. It is best done by putting a grid powered charger on the battery that can provide initially, about 10% of the amp hour capacity.
But some grid powered chargers might goto too high a voltage, which might possible damage sensitive electronics, so the battery should be disconnected from vehicle, but that can also cause issues depending on the vehicle. Just something to be aware of.
There are actually 3 types of Flooded lead acid batteries. Starting/lighting/ignition batteries, Marine/RV/Dualpurpose batteries, and then the venerable expensive, hard to actually acquire, true 12v deep cycle battery.
The Dual purpose marine battery is a starting battery which is more tolerant of deeper discharges. It has slightly lower CCA ratings. It loves all the marketing labels thrown on the side of it. I suspect many marine batteries are just starting batteries with a 15$ sticker on them, and some threaded posts in addition to the normal automotive studs.
As far as the OP's vehicle seeming to start perkier after needing a jump and then a 15 minute drive home, There is no way the battery got fully recharged in 15 minutes.
Now here is my personal opinion from living off battery power for longer than I like to admit. Much of the traditional battery recharging methods handed down by grandpa, mainly the low and slow trickle charge being best, are false.
Many/most battery manufacturers have a minimum charging current recommendation, at least for their deep cycle flooded batteries, and none of them say feed them as little current as possible for as long as possible to recharge. Generally the recommendation falls from 10 to 20% of the amp hour capacity measured in the 20 hr rate.
Meaning feed a depleted 100 amp hour battery a minimum of 10 amps initially for that 10% rate.
I have one battery right now, Albeit a true deep cycle battery, which wants that 10% rate, however when discharged, and I allow my alternator to feed it, the battery will initially take a 50% rate, and higher, if the rpm's are there to provide it. This battery being blasted, even briefly, with a much higher than recommended charging rate might shorten its life, but it holds higher voltages through the next discharge cycle, compared to the solar's low and slow to full charge over longer periods.
So I believe it is possible as one other poster indicated that this battery was partially sulfated before needing the jumpstart. The Sulfates blocking electon transfer and making the battery seem a bit dopey.
After the jumpstart, the battery was thirsty for amps and took everything it could which the alternator could provide for those 15 minutes, in which the battery was also physically agitated by driving motions. This amp blast and physical agitation knocked loose the hardened sulfate on the plates allowing it to settle on the bottom of the cells, exposing fresh plate material to transfer electrons and even being less than fully charged the next day, seemed perkier than the day before.
Even though 15 minutes of driving was nowhere near enough to fully charge this battery, the surfaces of the plates were less obstructed by hardened sulfates and so it now seems Zippier.
That sulfated plate material which got knocked off the plates is now resting on the bottom of the cells. That material was part of the batteries electrical capacity, so while the battery just lost capacity, it has increased the surface area on the plates returning a higher CCA rating and a perceived zippier starting experience.
The battery might last for years longer, if it is put on a grid powered charger, or it could die tomorrow if so much shedded plate material fell off that the cell might short out. In general Starting batteries are very intolerant of deeper discharges and a deep discharge halfway through its lifespan will kill it in short time. But if it was promptly and fully recharged at a reasonable rate, it might not have lost much capacity at all.
It is the slow discharge to dead, and sitting there dead for a while which really is the battery killer.
All lead acid batteries want to live their lives as close to 100% fully charged as possible. The battery owner who is aware of this, and that the alternator is not a magical near instant battery charger, and employs other methods to return a battery to 100%, will enjoy long battery life, probably. Some people never discharge the battery much at all and the vehicle's charging system keeps the battery above 95% and enjoy long life spans.
Note AGM batteries are different, as even if designed as a deep cycle battery, they can still provide huge CCA ratings. When deeply cycled, AGM batteries like Odyssey in particular, want a large current to recharge. A hundred amp hour battery initially wants 40 amps until 14.7 volts is reached. 14.7 volts it then to be held for 4 hours as the current required to hold 14.7 tapers down low.
Without meeting this recommendation, A deeply cycled Odyssey AGM will never reach full energy density, Despite that highly rated chromed alternator under the hood and the chest thumping confidence of the owner of said chromed alternator. According to an Odyssey tech I spoke at length with, it would require 2 more cycles, being drawn below 50%, then recharged at that 40% rate and 14.7 held for 4 hours, before full capacity was restored. Even without this proper recharge regimen on an Odyssey, it will still likely outperform a flooded battery, and for nearly 3x the price, it better.
I feel this is also true of flooded lead acid batteries to a much lesser degree. Without any backing data or engineers on my side, I feel a deeper discharge and a prompt and full recharge at a 10 to 20% rate is like a slap across the face followed by a cup of coffee to a battery which got bored of life in the 75 to 85% charged zone.
The thing is the slap and the cup of coffee might send a weak battery with no constitution to the recycler. The thinner the plates, the more likely that this aged battery will get all petulant at this treatment and quit.
To the OP, I'd recommend carrying jumper cables, and acquiring an Automatic battery charger in the 6 to 10 amp range, and letting it do its thing over night. If you ever do deplete the battery again, make sure to use the battery charger again promptly, and not rely on the alternator for a true full charge, unless you are driving for 500 miles.
