To be clear, just because a strap is advertised as a "recovery" strap, does not inherently mean it will stretch. In fact, google "recovery strap," and most products will not advertise any stretch at all, even they are indeed a properly-rated strap. However, what they all have in common is a very high working load / breaking strength, which is necessary even for carefully-executed recoveries because vehicles can shift and bind. They can still double as tow straps in that they enable you to apply smooth, even pressure to pull a vehicle without it trying to "bungee" or, just as importantly, without damaging the strap by keep it stretched out for an extended period. One examples would be pulling a broken-down rig several miles out of a trail; you wouldn't want an elastic strap because it would have a tendency to "slinky" the towed vehicle, and you'd potentially damage the strap.
Still, they are not meant for deliberately jerking the strap with the recovering vehicle!!!! For those, you'd want a kinetic recovery strap, also called a "snatch atrap." A snatch strap allows you to use the vehicle's momentum to generate extra force to recover the vehicle, without generating the tens of thousands of extra pounds of force created by jerking a stiff strap or chain.
So, sometimes a non-elastic recovery strap and a kinetic recovery strap can perform the same duties. If slowly pulling a sedan out of a ditch, either would work. On the other hand, a non-kinetic strap should be used for lighter-load, extended pulls, while a kinetic recovery strap should be used for hard recoveries requiring dynamic movement to "snatch" the stuck vehicle out.
Hope this helps!