Do spells with a range of “Self” target the caster?

New to D&D, and thought about creating a Beast Master. I was wondering if spells with a range of “Self” would count you as the “target” of the spell. There’s some debate in my group, as unlike something such as Cure Wounds, which specifies “A creature you touch,” there’s technically no mention of a target in a Self range spell within the description. A fair amount of people in my playgroup come from a TCG background, where the presence (or lack thereof) of keywords like “target” are essential for determining interaction.

tl;dr Would Paladin Smites or Thunderwave count as “targeting” yourself, and therefore be affected by Beast Master’s Share Spell?