Proficiency with specific weapons vs 'simple and martial'?

Question

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?

Answer 1

A character proficient in simple and martial weapons is proficient in all PHB weapons. For them, other individual weapon proficiencies (like Dwarven Combat Training) don't do anything. There's no difference between a Human Fighter and a Dwarven Fighter in terms of weapon proficiencies.

However, some classes only get a limited number of weapon proficiencies, and this is where racial or other weapon proficiencies come into play. For example, by default a Wizard is only proficient with daggers, darts, slings, quarterstaffs, and light crossbows. A Dwarven Wizard, however, would also be proficient with battleaxes, handaxes, and throwing hammers thanks to Dwarven Combat Training. For that character, the Dwarf's additional weapon proficiencies greatly expand the list of weapons they can use effectively.