EDIT: My answer below is really naive and may contain inaccuracies/broad generalizations. Here is a better, more robust post from GATK: https://gatk.broadinstitute.org/hc/en-us/articles/360035890491?id=11127
I'm going to take a shot at answering this:
Somatic variants = variants seen in a somatic cell not seen in other somatic cells. Somatic cells are not inherited by offspring. Germline variants = variants seen in germline cells that are passed on to offspring
Somatic and germline, as you can see, are based on which cell the genetic material is extracted from. Indels are a type of mutation that can occur anywhere.
Tumor normal is considered somatic as cancer is usually an abnormality in the somatic DNA, corrupting one particular cluster of cells in your body, rendering them with a different genotype than the rest of your body.
I was wondering what exactly is the difference between germline and somatic variant calling?
Germline variants are either diploid/biallelic, so expected alternative allele frequency is 50% for a heterozygous position. Somatic variants depend on the tumor purity and are not present in all cells tested. As such variant allele frequencies can be much lower.
Why is a tumor-normal study considered to be somatic?
Because you are looking for differences between the tumor and the normal sample, and therefore variants which are not part of the germline but appeared somatically.
Can indels be picked up on germline or somatic samples?