Usually, better tools are more expensive than less effective versions. So the lumberjack (from the earlier examples) will need to have enough resources to buy a chainsaw. The production of a chainsaw requires much more roundabout methods that does an axe, to manufacture it. It has also required more capital and labour for its production. If the lumberjack spends his entire income each day, and saves nothing, then he will be unable to buy or build the chainsaw. He must save, or ask someone else to provide him with the necessary credit (which is somebody else’s savings), or ask another investor to come on board and buy the chainsaw. Without these saved resources, he will be unable to acquire the tools which will permit his greater productivity and he will not become more productive.
Whatever method he uses to acquire the new Capital equipment, someone needs to have saved enough to produce the tool, so that it can later be exchanged for other goods. It may be that the chainsaw manufacturer himself will give the lumberjack the credit, but in this case the chainsaw manufacturer needs to have the savings, necessary to transform raw materials into a chainsaw, and then sustain himself until some agreed time in the future.
Real saving can only be achieved by producing more than what is consumed. If no-one in the society saves, then no credit or investment funds will be available. An investment uses saved resources to produce tools. The investment involves the spending of saved resources, but it aims at producing consumer goods in the more distant future. Instead of consuming something today, the funds are spent building something which will hopefully assist in producing more in the future.
Consider automobile production. A small team of specialists may be able to produce a few cars per year from a workshop. The amount of capital in use is relatively small. The cost of building a bigger factory to produce hundreds of cars a day would be much greater. The time from turning the first sod in the factory and getting the first car out will take longer than producing a car from a small workshop. Factory produced cars may cost less to build but far more cars need to be produced to make the investment pay. This factory requires far more investment and thus much greater savings to build.
Primitive societies struggle to save, because the goods necessary to survive are so scarce. People are not sufficiently productive to create a significant surplus, so savings are extremely limited. A hunter gatherer may be so inefficient at food production, that he may be capable of only providing sufficient food for himself at a subsistence level. His life may threatened daily by thirst, starvation and exposure to the harsh environment. Once savings start to rise, and tools to enable greater productivity can be created, an individual will become more productive and more capable of saving.
Some people save but do not use these savings to for any investment purpose. A person who saves his overproduction may hoard that for some future catastrophe so there is a possibility that saving will not always produce an investment, but investment cannot happen without saving. The great advances in reducing scarcity since the beginning of human civilisation, have been driven by savings and investment, which enhance Capital accumulation and increased productivity.