The two types of energy absorbing buffer stop. One type is the previously mentioned hydralic buffers. The other type uses friction as they slide along the rails. AFAIK all buffer stops at termini or bays used by passenger trains must be energy absorbing. The ability to stop a train without damage to the train or injury to the passengers varies depending on the speed of the train, it's weight and also the design of the buffers. Modern installations are always friction type (take the ones at St Pancras for example).
As far as the actual trains go, the buffers on trains provide very little energy absobtion. They are designed to absorb the slight energy when buffering up at very low speed, or as vehicles bump together on loose coupled trains. Buckeyes, Dellners and other automatic or semi automatic couplers also have the ability to absorb energy, infact modern couplings have a two stage system, the first being able to absorb minor forced when coupling up, the second designed to give way in the event of a collision so the coupler will absorb some impact and then transfer the impact to the main body of the train which will be provided with anti-climb devices (the corrugated effect seen on some types, on other types they are behind fibreglass coverings that would themselves be destroyed in a collision. They are also seen on many buffer stops).
As for speeds, I think modern buffer stops are designed to stop a train with minimal damage to the train and minimal risk to passengers at about 10mph (probably a factor in that being the speed TPWS is set at approaching buffer stops). Particularly on trains (or buses) where passengers can be standing (especially approaching stations, where buffer stop collisions occur), a sudden stop from every very low speed has a high risk of injury. A person falling from standing is at a reasonable risk of serious head injury, even fatal, not to mention broken hands or arms, and in the elderly broken hips. A sudden stop that displaces luggage or other heavy or dangerous items can also cause injury, possibly serious. There was an incident fairly recently on a bus where the driver had to brake hard and a passenger who was walking down the bus fell and banged their head, sustaining fatal head injury.
