Somehow, Short-tailed and long-tailed suggest only if the claims are reported and settled quickly or are delayed. But these are used everywhere in General Insurance.
Short and Long tailed is an important concept there is not an exercise in which we are not going to use it, consider pricing, reserving or even Asset Liability Management.
Short tailed means that the claims are generally reported quickly and settled quickly by the insurer.
Long tailed means that there is a sizeable proportion of total claim payments that takes a long time to be reported and/or a long time for the insurer to settle.