> English "th" represents two different sounds

Three main ones (excluding compounds where it's really a “t” next to an “h” that aren't related): in IPA terms, they are θ,ð, and t.

> and English speakers manage just fine, because in its sound system they are totally distinct and never confused with each other.

English speakers do okay because they learn fairly quickly that written English isn't phonetic and you just have to memorize spelling, not because of a lack of ambiguity.

Nothing about “Thai” vs. “thigh” vs. “thy” tells you which “th” sound each uses (and in pronunciation, the “th” sound is the only difference between them) except knowing what each word is as a rule unto itself.