Adept is a spell grading
You are given most spells at grade Apprentice I
You can buy Apprentice II at your local scribe
Apprentice III and IV are player made
Adept I is a chest drop in appropriate level zones
Adept II seem to be the special training spells you are given
Adept III is crafted by players from rare components
The higher the grade the more effective the spell (broadly speaking) and it replaced your current version. If you scribe Minor heal Adept I you can no longer cast it at lower grades. Some spells this matters more than others. I've seen Summoners claim that their App III scarab is better than the Adept I spider.
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Wherever I go - there I am.