It's impossible from a picture: look up "how to identify wood finish" on Google

At least you found floor! Those are in good shape.

Here is a link that might be useful: Bath floor fixing

A light sanding after you get the patches done, some careful staining to blend colors and a good top coat ... you will be looking GOOD.

I'm pretty sure it's a wax finish. It dulls (whitish film) when I put DNA or white spirit on it.
If it is a wax finish... is there a way to blend the new to old *relatively* seamlessly? Is it likely to just be wax, or wax and stain, or wax and shellac, or wax and oil?
I'm going to add here that under no circumstances would I sand the floor... I love the original, unsanded finish. It has tons of character that I want to keep. I also don't want a polyurethane finish.
Thanks for your thoughts.

I'm guessing from the floorboards and the woodwork that your house is pre-1930 and most likely pre-1900 -- is that right? Are your baseboards oak also, under those coats of paint?

The wood of the floor was mostly likely sealed (maybe amber shellac, maybe varnish) before the wax was applied. It's hard to do a wax-only finish on oak, because of the open pores.

So, I think you would have to strip the wax off an area that extends beyond the part you are trying to repair. Use mineral/white spirits and 0000 steel wool, followed by the spirits on a clean cloth until you are sure all the wax is gone. Then, extending a little beyond the area you are trying to blend in, use denatured alcohol to strip off the shellac -- if this doesn't strip it, it isn't shellac. If it does strip it, you can blend in a new shellac in that area. Either mix your own using amber flakes or buy a pre-mixed shellac -- make sure it's fresh. Apply it sparingly until you get a color that matches the other de-waxed shellac. Overlap the edges slightly; the new shellac will melt the old to blend the edges. Let it dry thoroughly and apply a top coat of wax.

Thanks, Chibimimi
The house is 1906, but I'm pretty sure the baseboards are not oak, sadly. From what I can tell, all the woodwork expect the handrails on the stairs and floors, are something less grand and covered in an oil and shellac fake graining paint job.
I wonder: If the base coat is not shellac, what else might it be? Also, any recommendations on choosing a wax? Would any wax do or do you need one that matches the existing finish?

As PPs have said, what you probably have on the floor is either shellac or varnish, covered by wax.

Test the finish to see which it is.

The shellac or the varnish *is* the finish. The wax is to protect the finish. In the olden days, the wax was removed and replaced with a new coat regularly. The interval depended on the amount of traffic in a given room/area, but it was probably done at least once a year throughout the entire house.

Shellac especially can be damaged by water--white spots will form. The wax adds a layer of protection for the shellac, and adds a nice soft glow to the floors, instead of the high shine of the polyurethanes in use today.

Shellac can be scratched, but it is also easier to refinish small spots than it is with urethanes.

So in your case, if you have a shellac finish, you can repair bare spots as Chibimimi explains. Then clean the old wax off the entire floor, and re-wax it. It probably needs it by now.

You can use paste wax, but it is a bit harder to apply than liquid wax, and takes more buffing to get it up to a good shine. The liquid wax is easier to apply, but doesn't last quite as long in high-traffic areas.

Here is a link that might be useful: how to clean shellac'd floors.

Thanks for your reply, camian.
I used some cheapo water-based wax stripper I got at the hardware store. It took some finish off, but stained surrounding (raw wood). And not much came off, even after 4 applications. Hard to say what, if anything, is underneath. I work a lot with shellac, and think I would recognize it, but there doesn't seem to be any.
I'd like to shellac and re-wax the floor, but this would require removing the wax... any thoughts on how to strip the wax more effectively? Are stinky mineral spirits the only option?

Denatured alcohol will remove the wax and shellac simultaneously. Careful though, it's flammable and can cause blindness.

Shellac and wax is a beautiful and easily maintained floor.

You can sand and refinish the floor without getting a "polyurethane" finish. I have oak floors in my 1940 colonial, and we had the entire 1st floor refinished so it would match the new wood we used to replace the linoleum in the kitchen.

By the time they got done you could not tell the difference between the new and old floor areas, and the finish was the same appearance as the low traffic areas on the unrestored 2nd floor.

If you want to make this floor look good you need to find a good refinisher who is used to working with old floors. They have all the tools and techniques, and they can do it relatively quickly. You do not want to use a company that mostly just installs new floors.

Bruce

Thanks for the replies.

Bruce - I have considered sanding, but it's the texture, not the appearance, of the floor that I want to preserve, so sanding is definitely out.

Trebuchet - I am surprised to hear DNA will remove the wax. I gave it a try in a few places, but it only clouded (white film) the finish and nothing seemed to be removed. Maybe there is a special technique, dwell time, etc?

My mother used to remove all the wax once a year from all the floors in our house using only a razor blade, down on her hands and knees. Lots of work but no chemicals.

Thanks, Marcolo. I think I'd like your mother!

I haven't had much luck with DNA removing wax, but mineral spirits and 0000 steel wool, followed by rags, does a good job. You need excellent ventilation, though, and must be careful disposing of the steel wool and rags to make sure they don't spontaneously combust.

This is for "real" wax, not the acrylic/synthetic type.