down payment vs part 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. 

part payment

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