Can somebody explain how are EV, and especially Tesla, batteries different from, say, my laptop batteries, which normally degrade to the point of being unusable within 4-5 years, and have to be replaced?
First, EV batteries typically have active thermal management. Heat kills lithium ion batteries. When you charge your laptop, the battery gets hot, and this accelerates degradation. When you charge your car, the cooling system engages and keeps the battery at the optimal temperature. (The LEAF doesn't have an active cooling system for its battery. It also suffers much worse battery degradation than other EVs. Coincidence?)
Second, EV batteries are somewhat de-rated from their full capacity. Lithium ion batteries don't like spending time at the ends of their capacity. They want to live in the middle, not be fully charged or fully discharged. Laptop and phone makers tend to view their products as short-lived, disposable items, so they'll optimize for maximum running time on the battery by charging to 100% and draining to 0%, at the cost of battery longevity. A car will wall off some of the capacity so that when you're at 100%, you're really at, say, 90%, and when you're at 0% you're really at, say, 10%. At least some of these cars take it further and let you limit the maximum charge so you only use what you need. For example, I normally charge my Tesla to 90%, which is all I need for 99% of my driving. When I need that last little bit, I can charge it all the way to 100%.
Third, a large portion of degradation comes from the number of actual cycles you use, and deeper cycles are worse. A typical battery might last 300 100%-0% cycles before it degrades beyond usability. If you only use 50% of the capacity each time, then it might last 800 cycles. (Very rough number, totally pulled out of my nether regions, but you get the idea.) Long-range EVs are typically not driven to the limits of their range every day, so the batteries are treated well. Most days, my car might go from 90% to 80%, then get charged back to 90%. My phone, by comparison, goes from 100% to around 20% and back to 100% each day, which degrades the battery far more.
And when they're no good for that they're recyclable. Although currently it's cheaper to dig lithium out of the ground than reclaim it there's other stuff (cobalt particularly) that is reclaimed.
While they may share some aspects, the two were designed for dramatically different a) price points, and b) use cases.