Looks like some incomplete information going on here.
Tree saver
Tow strap
Tug strap
All different in construction and application.
Tree saver is to SAVE THE TREE. Zero stretch. Usually on the short side - 6 to 10' in length. Typically on the wider side 4" or so.
Tow straps have minimal stretch and are designed for just towing a vehicle NOT RECOVERY. I very rarely see these available. 2-3" wide typical.
Tug straps may look identical to tow straps, but they have alot of stretch. These are designed for recovery. The energy of the moving vehicle stretches out the strap and that built up energy pulls out the stuck vehicle. The stretch also takes some of the shock impact out of the recovery. Usually 2-3" wide and 20-30' long.
A strap that stretches and is wrapped around a tree does two things. Firstly, strips the bark off the tree and kills it. Second it stretches and can tighten on the tree and in some cases gets stuck there depending on how it was wrapped.
Hope this helps.
Kudos to you man!! You are the only one to give a correct answer.
Chiromancer, I hope you haven't opened and used your "tow strap" yet, it is strictly a tow strap and should NOT be used for recovery. Recovery straps have an elasticity factor which allows you to pull another vehicle out gently and properly without the shock that is caused by a strap with no elasticity like a tow strap, (it is the shock or jolt that a vehicle will receive damage from.) A tow strap has about 0 to 2% stretch factor, a "snatch strap" has about 10% stretch factor and even better is a kinetic recovery rope which has a stretch factor of about 30%. The more stretch factor the more gentle and safe the pull will be, it is the kinetic energy stored in a strap that does the work and does it safely.
Here's a great video, [edited] unfortunately he didn't cover tree savers but a tree saver should be like a tow strap with no elasticity. You DON'T want the tree saver to stretch (NEVER use a recovery strap as a tree saver), if there is stretch and the cable breaks that stretch is going to turn something in to a projectile.
Anyone who wheels SHOULD have both a tree saver and a recovery strap (snatch strap).
Happy and SAFE wheeling!
Jeff