taru-adjective, adverb taking the 'to' particle
Describes thick fog, smoke, dust, or similar obscuring conditions. Often used with と (もうもうと) as an adverb.
工事現場は砂埃でもうもうとしていた。
The construction site was thick with dust.
濃霧がもうもうと立ちこめ、視界が悪かった。
Dense fog hung heavily, and visibility was poor.
taru-adjective, adverb taking the 'to' particle
Used for mental states where thinking is unclear or consciousness is foggy, often from fatigue, illness, or intoxication.
熱で頭がもうもうとして、考えがまとまらない。
My head feels hazy from the fever, and I can't think straight.
濃い is a general i-adjective for 'thick, dense, concentrated' and can describe liquids, colors, or density, while もうもう is specifically for obscuring atmospheric conditions or mental fog.
ぼんやり can describe both physical vagueness and mental absent-mindedness, but もうもう emphasizes a thick, enveloping obscurity rather than mere indistinctness.
Reduplicative mimetic word; the exact derivation is uncertain, but it is associated with the idea of something spreading thickly and obscuring vision or thought.