A stripped thread is one in which the threads of the bolt or nut or both have become so damaged as to be incapable of holding the loads for which it was intended. One can strip threads by over-tightening until the nut or bolt head turns but no additional force is applied to the joint being fastened.
Such damage is often visible as an area of smaller diameter, as the "raised" threads are gone.
Cross-threading is usually caused by the fastener being applied at an angle to the proper position and being forced onto the bolt. The threads of a bolt or nut are designed to engage with the axis of each aligned, which allows the peaks and valleys of the threads to slide across each other.
If the bolt is applied at an angle, the threads can engage the nut or threaded hole in such a manner as to cut through the existing thread, creating a poorly sliced section. As the bolt is turned, it will proceed into the hole, but typically not straighten out and will eventually cease to progress.
Another way of creating cross-threading is to use the wrong match between nut and bolt. If a quarter-twenty bolt (1/4-20) is forced into a quarter-twenty-eight hole, one can manage to have proper axis alignment, but incorrect threads. It's possible to drive the bolt into the nut to the fullest extent, but the threads on both are likely to be mangled, damaged and not provide rated strength. In some cases, the damage is sufficient to prevent extraction. Either way, the damage can remove the fastener from service.
You can cross-thread a fastener and tighten it sufficiently so as to strip the threads. If it happens deeply enough in the assembly, it may not be possible to extract, as the threads would have been damaged and no longer function as intended.
Almost all of the above comes from having experienced both situations.
Image above credited to tribology-abc.com