In the PHB on pg. 146 it states that there are two weapon categories in which the players can be proficient: simple and martial.
As per this answer to another question, being proficient in either category makes the players character proficient in using all weapons of the respective category.
However in the race descriptions the players are given proficiency for specific weapons. Dwarfs, for example, have the trait Dwarven Combat Training giving proficiency with battleaxes, handaxes, throwing hammers and warhammers.
How do the two types of proficiencies interact with each other?