I'm not doubting your description of "screening"....(OK, yes I am just a little
)
Screening is basically a cut and polish of your existing hardwood floors they must have had a previous coating of polyurethane. Think of it like cut and polishing your car it will remove SMALL scratches. Polyurethane MUST be applied after the "screening" or your floors will look really bad.
If your floors are not in bad shape just need some"sparkle" added back into their life then screening is an option.
Notes to remember before paying for just a quick job:
As wood is VERY porous any product applied to it in some way is absorbed into the grain of the wood, stains obviously are absorbed fairly deeply, polyurethane moderately and wax some what to the surface layer.
ANY unsealed floor, will over time absorb everything from water dropped or brought in on shoes to simple household moisture in the air, this is one of the reasons interior unfinished wood changes color without any direct sun.
Nowadays very few wood floors are "waxed" as the upkeep is tremendous, almost all are layered with polyurethane as a finish from satin up to high gloss, to do this correctly you need to sand the floor back, any impurities or stains must be removed or they show up 10 fold when a finish is applied.
The main reason floor sanding is not cheap is that it must be done in at least two layers, first a rough sandpaper is used to remove of any stains and the highs and lows of a floor, then a finer grade paper is used to bring the wood to a nice smooth finish. The amount of passes a floor sander has to do is relevant to 1. how bad the original floors are and 2. How good a finish you want on the floor.
Also remember "screening' will not bring all floors back the same, if you have an area that is very badly worn it will look different from any other area immediately around it after a quick refinishing. The ONLY way to avoid this is to refinish the entire area by sanding.