These terms are used so often, yet the meaning of them and differences between them are generally not very well understood so here is a short post that "was" intended to provide some clarity.
Compost is the intentional accumulation and placement of organic matter, the aim being to accelerate the decaying process. The intentional part is important. Dead stuff on the ground is NOT compost, just decaying organic matter. It is the controlled, or semi-controlled conditions that make it compost.
Compost, even if mature, is still breaking down and supplying nutrients. When applied in your garden it has the immediate effect of adding nutrients available to plants and bacterial components that contribute to a healthy soil food web. As the seasons progress and decay continues, it eventually converts to humus.
Humus is supposed to be a stable organic component, the result of the decay of organic matter whether that be natural decay or, as we see above, decay during composting.
Humus being stable cannot be penetrated by microbes and is greatly resistant to further decomposition. Thus stable humus adds few readily available nutrients to the soil, but plays an essential part in providing its physical structure.
Humus improves soil structure (and texture) and has remarkable water retentive properties.
Humus has a high cation exchange capacity (CEC), which means it acts as a storehouse for plant nutrients not allowing them to wash away (leach) from the soil with the water passing through the soil. High CEC is why humus is regarded as being fertile.
Since writing this post it has come to light there is a debate regarding the existence of humus. Humus may be extinct.
Needless to worry it's still super easy to build great soil.
Add plenty of organic matter to the soil via chop and drop mulching, manures and composts
Keep soils inhabited with diverse communities of living plants at all times and mow and prune these plants to encourage root shed that add to the soil organic matter.
Avoid any compaction to the soils you are cultivating - by foot or machine.
Keep soils well hydrated - like a moist sponge is perfect
Don't waste your money on nasty products such as Roundup.