Compost and compost tea is not fertilizer, but infrastructure for your soil. This is really good place to start with learning how the Ecology and Phenology in soil works. We start with what we know and branch out.
Definition of fertilizer: Fertilizer is made of a salt consisting of Ammonium (NH4) & Nitrate (NO3). A salt is a set of molecules that dissolves in water. Or it’s water soluble. Table salt is made of Na and of CL. Both dissolve into water. One part of the salt has a slightly positive charge and the other a slightly negative charge. Opposites attract. The bond between the salt atoms is not that strong. When dissolved in water, water pulls them apart.

Definition of Fixed Nitrogen: Almost 80% of air we breathe is made of N2. Or just plain nitrogen. The attractive bond between two atoms of nitrogen is too strong to be pulled apart by water or other means. In short, nitrogen is one of the building blocks for plants to grow, but it is not directly absorbable by plants. It needs to be combined with something else to make the bond weak enough for plants to absorb it. It needs to be fixed to another set of atoms with a weaker bond. In general, there are a number of fixed nitrogen molecules. The most common molecule is called Nitrate (NO3, notice one nitrogen atom, not two). This molecule is one part of the fertilizer salt molecule. The other part of the fertilizer molecule is Ammonium (NH4). Both molecules are created naturally by soil micro biology. Below is a link to some of my pages where you can see a variety of ways Nitrates are made using microbiology and plants alike. In general fixed nitrogen is in some part of a biological cycle usually involving a number of different species of plants, bacteria and animals. I’m not going to repeat is here because the webpages have great detail.
For expanded information on Nitrogen Fixing Cycles, Click here
Fertilizer gives plants exactly what they need without microbiology. This short circuits the microbiology and dies off. As a result, you are required to continue to use fertilizer because the soil does not have any remaining infrastructure to produce fixed nitrogen. This applies to synthetic fertilizer and to organic fertilizer. Both create the same results in soil.
Last note, what happens to NH4 in fertilizer if only NO3 is used? NH4 is absorbed using a Nitritifying bacteria. This bacteria eats NH4 and produces NO2 (or Nitrite, it is Nitrate with a “i” and one less oxygen molecule). Another bacteria turns NO2 into NO3. So, both halfs of fertilizer salt is used, but only when the microbiology is present. Most of the time it dies off. That is why fertilizer has a huge impact on plants when first introduced. Afterwards, only half of the fertilizer molecule is used and the rest this thrown away. Where does it go? You have seen it before…… Have you ever seen the white stuff that appears on clay flower pots after a year or so? And you can put the flower pot in water to dissolve/scrub it away? That is leftover NH4.