Can anyone re-assure me? Is there anything that lets car batteries last significantly longer than phone batteries?
The individual battery cell has a pretty hard limit on the number of times it can be cycled (i.e. discharged and recharged). Your typical AAA NiMH rechargeable has a lifetime rating of about 100 cycles I believe.
If a battery pack has multiple cells, they can be connected to each other in parallel or in series (and any combination of the two choices). In series gives you more voltage (i.e. kick), in parallel gives you more amperage (i.e. duration).
If the electronics hooked up to it are "smart" then any parallel sets of cells in the battery can be charged separately. This means that the laptop might drain parallel set A down to 30%, set B down to 50% and set C down to 90% leaving you at an overall percentage of roughly 56%. If you then hook the charger up, the laptop will charge the lowest set A first, then B, then finally C. If you stop charging before it gets to C then you've saved an entire charge cycle on that set which means it lives a little longer.
So.. now on to the Tesla. It has 8640 individual cells wired into 16 parallel sets of 540 in-series cells. The car will selectively drain and charge each individual set to maximize the life of the battery.
By default the car also does not charge the battery to 100%. The default is 80% which gives you a typical range of about 230 miles. That leaves more choice to the charger about which parallel sets to charge without reducing the life of sets that are nearly full by topping them off.
If you are going on a long trip, you can put the car in "range charge" mode which will force it to top off to about 260 miles of rated range.
The predictions based on modeling so far is that the battery should retain over 80% of its total capacity even after 8 years of typical use.
Follow up question. How does the regenerative braking affect battery life? It seems like you be charging and discharging quite a bit just during normal driving?
One thing different is they have you always leave the car plugged in when not in use as much as possible so they can manage temperature. They also slow charge after ~80% which most phones won't do.