The short answer is that the germline model assumes a diploid sample with corresponding allele frequencies. The tumor-only model assumes the variant could occur at any allele frequency. The best starting point for a high-level overview is the user guide:
And the methods writeup for more details:
This is a latex doc you'll need to clone and render for the latest version. As described above, the supplement provided with the pre-print or final publication are both very good starting points.