Not completely right
(5.5e) Two-weapon fighting is a Fighting Style that only some classes can get.
Dual Wielder is a general Feat that any character of level 4 with str or dex 13 or higher can take.
Anyone can dual wield when their main weapon has the Light property.













That is true, for the 2014 (5e) version
The 2024 / 5.5e version rules no longer have the “two-weapon fighting” subsection - the rule is now merged into the description of the ‘light’ weapon property