There are 5 main damage types in Dark Souls 3. Physical, Magic, Fire, Lightning, and Dark. The Physical damage category can be further split into it's sub-types, which include Standard, Strike, Slash, and Thrust.
The AR (Attack Rating) of your weapon is displayed in the stats screen. The number shown by this AR is an approximation of how much damage your weapon will deal to any given enemy in a single attack. However, there are various factors that can affect your actual damage output, such as enemy damage absorption ratings (armor), weapon moveset modifiers (light vs. heavy attacks), damage buffs (spells and/or rings), and situational modifiers (counter damage, ripostes).