What actually happens to the concrete
A car driven on salted roads brings a startling amount of salt solution home, packed into wheel arches, sitting along the sills and clinging to the underbody. Park it in a warm-ish garage and all of it melts off onto the floor overnight. What you spread on your own driveway adds to that, and some chemistries add more than others.
Concrete is porous. Salt solution wicks into the surface, and then two separate mechanisms do the damage. Water in the pores freezes and expands, and salt crystals grow in the pores as the solution dries and re-wets. Both push outward from inside the concrete. The result is spalling: the surface flakes and pits, exactly as you see on the aprons of older garages and on parking structures.
This is not a cosmetic problem. Once the surface is open, water gets in faster, and on a slab with reinforcement near the surface it eventually reaches steel. Resurfacing a garage slab is contractor work.
The comparison, stated plainly
A full-length containment mat is roughly $70 to $160 depending on size, and it lasts multiple seasons. Resurfacing a two-car garage slab is a four-figure job, and patching spalled concrete well enough that it does not simply spall again next winter is genuinely difficult.
The mat is not a cheap version of protecting the slab. It is the only affordable version.
What separates a containment mat from a tarpaulin
Two layers doing two jobs. The top layer is absorbent, so meltwater is held in the fabric rather than sitting in a puddle you walk through. The bottom layer is waterproof, so what the top layer absorbs never reaches the concrete. A plain tarp has only the second property, and water pools on it, runs to the edge and off onto the floor — which is exactly the thing you were preventing.
The specification you would want to compare is absorbency per square foot. Nobody publishes it, so we say that on both entries below instead of estimating one.
Full length or half length?
Most of the drip falls off the front of the car: the engine bay is warm, the front wheel arches carry the most slush, and the front suspension is a tangle of surfaces for it to cling to. A half-length mat under the front of the car catches the majority of it for roughly half the price.
Go full length if you park a longer vehicle, if you have rear-wheel arches that pack with snow, or if the floor already shows the fine pitting that means spalling has started. At that point you are protecting a surface that is already compromised, and partial coverage is a partial answer.
Skip this
Skip the cheap PVC 'garage floor mat' rolls sold for looks
The thin glossy roll-out PVC flooring sold for garage appearance is not a containment product. It is not absorbent, so water sits on top; it is not sealed at the seams, so water runs underneath; and water trapped under an impermeable sheet against concrete is worse than water on open concrete, because it never evaporates. If the purpose is protecting the slab from salt, buy an absorbent containment mat, not a floor covering.
The free half of this job
A mat catches what falls off the car. It does nothing about what stays on the car, which is the part that rusts the vehicle itself. The two go together: a mid-winter underbody wash on a day above freezing removes salt from the places you cannot reach, and the mat catches what the drive home shakes loose. The order to do both in is here.
Catching the meltwater also matters for the air in the garage, because water that sits on a cold slab evaporates into the room and condenses on the coldest metal in it. What actually works to dry a cold garage starts with not letting the water spread in the first place. And if you are considering sealing the slab properly rather than covering it, the coating comparison turns on a temperature window that is closed for most of the year.