As convenient as it would be, there really is no "one size fits all" with working blades. We've covered how to choose and use knives to great extent. In the area of larger blades, however, we've only just touched the surface. As having the proper blade for these is even more important, a bit more discussion is called for.
Axes are big and heavy, featuring handles in excess of 2 feet, and heads weighing 2 pounds or more. Special axes, called mauls, can have heads weighing over 4 pounds. This length and weight gives them incredible leverage, making them ideal for medium and large wood splitting tasks. With work and practice, axes (not mauls) are also well suited to felling trees, a task they've performed for most of their existence.
The big downside to an axe is its size. It's too long to pack while carrying other gear, and 3-6 pounds is a fair bit of weight to carry. They're also quite a workout when used for cutting, as opposed to splitting.
A hatchet has most of the pluses of an axe without the major negatives. Hatchet handles are 12-24 inches in length, with light heads weighing in at roughly 2 pounds. They lack the leverage to do heavy splitting chores, but for light and some medium splitting, they do a very good job. Their short length means they fit easily in a pack or on a belt, so they're far easier to take to remote locations.
Their limited size and weight means that hatchets are worse than axes for cutting tasks. They'll cut small branches well enough, but anything thick will consume time and energy in job lots.
There are a plethora of saws available, all suited to different tasks. For outdoor or in-the-woods use, my two favorites are bow saws and folding saws.
Bow saws make short, easy work of downed trees, brush piles, and other medium wood. They can even be used to handily cut down small and medium trees. Their bow shape makes them very efficient and easy to use, but also causes them to take up a fair bit of space in a pack or bag. There is also the difficulty of keeping a guard over the blade to prevent damage and injury.
Folding saws address both of those concerns. The blade folds into the handle for storage, and locks open like a giant serrated pocketknife when in use. The blade on a folding saw is much smaller, however, and the design leads to less efficient cutting. 2-4" limbs are about the limit of what a folding saw can successfully cut. This is often plenty of capacity, but it is a limitation to keep in mind. The up side of the folding saw is that, when folded, it often takes up no more space than a large knife.
Splitting the difference between a folding saw and a bow saw is the Sven Saw, because the Swedes had to come up with something cool to match the Mora. It has all the benefits of the bow saw, with a large efficient blade and easy cutting stroke, while folding up nearly as small as a folding saw. The only downside to the Sven saw is that it uses a proprietary blade, so you have to plan ahead a bit if you notice your blade getting worn, or else keep a spare on hand.
The other big concern about all saws is blade maintenance. Sharpening an axe or hatchet is incredibly simple, and can be done with the same coarse stone you use for your knives. Sharpening a saw blade takes tools and skill. If spare blades are available for your saw, keeping a couple on hand may be a worthy expenditure. If not, a bit of research into your specific blade and how to sharpen it is in order.
As with so many other things, pick the proper tool for the job, to get it done quickly and safely.