advance payment vs down payment

advance payment

noun
  • The part of a contractually due sum that is paid or received in advance for a good, service or social security payment. 

down payment

noun
  • A payment representing a fraction of the price of something being purchased, made to secure the right to continue making payments towards that purchase. 

  • Any initial commitment signifying an intention to carry out a larger future commitment, even though no legal rights or obligations are secured. 

How often have the words advance payment and down payment occurred in a corpus of books? (source: Google Ngram Viewer )