Sometimes it is hard to distinguish what people call bushcraft, from any other type of camping or backpacking. I personally do not think there is any need for such distinctions, but there are a few tools, which are often found in the bushcrafter’s bag, but are missing from that of the backpacker. These tools allow a person to more directly interact with the environment.
In the northern forests, these tools most often include a knife, a chopping impliment, and a saw. One popular combination of tools following this pattern is featured in the below picture. It is favored by Ray Mears, and because of his endorsement, has gained wide popularity in the bushcraft community.
It features a knife of fairly small proportions, no longer than 6 inches, but most often around 4 inches in length. Many these days prefer a Scandinavian or single bevel grind, but it is in no way required or even necessarily preferred. The most important part is that the knife be comfortable for you to use.
The second tool is a small axe, with a handle no longer than 20 inches, and a head weight around 1.5 lb. The Gransfurs Bruks Small Forest Axe has become the standard for these axes.
The last tool is a small folding saw such as a Kershaw or a Bahco Laplander.
This combination of tools allows for completion of a wide range of tasks, from fairly heavy woodworking such as chopping to fine work like carving.
The picture below features a variation of that combination, and is the one I have been finding a lot more useful.
The combination features a knife, a larger saw, and a small hatchet instead of the axe. The reason why I prefer this combination is that I find it much easier to process large wood with the saw rather than the axe. This reserves the axe/hatchet for carving and splitting. The hatchet fits that role much better for me. Again, the combination allows for the completion of a wide range of tasks in the bush.
In addition to the above tools, you may want to add some specialized tools. I like to carry a small 2-inch carving knife and a crook knife in case I want to do any delicate carving.
The tools you carry will always depend on the tasks you have to perform in the woods, as well as your local environment. There is no wrong combination as long as you can do the work you need to complete and do it in an efficient way.