All of the above.
The WWII Khukuri I have is an excellent chopping tool, but is a little scary looking when strapped to my belt, so it stays home unless I'm on private property where the public can't see.
My saw is a T handled combination wood and bone saw that was sold by Buck knives near 20 years ago. It came with a nice leather belt scabbard and is a joy to use. Nothing against the nice folding saws on the market today, but this one will be hard to replace. I bring it with me on most trips where firewood gathering includes limbing dead fall, or blow down trees.
I just picked up an S.A. Wetterling large hunters axe and I can see it coming with me, even when I'm packing in. It's relatively lite weight and smallish size make it a good pack axe.
BTW, after using the Eriksson Mora Swedish Army Knife that came with my axe, I prefer it over the Frost in many ways. Not the least of which, is that it's handle is a bit more flexible in use.
For day hikes, I don't carry saw or axe, but will have both with me when I'm packing in for an overnight or longer stay.