The ambiguities in the English language come from the imprecision of the user.
'Day' is a good example, today, this day, etc. are fine in general speech. But 'Day' can mean the period from sunrise to sunset on a particular date, or a period of 24 hours, (Either from midnight to midnight, or some other selection).
Confusion can be avoided by more careful selection from the language.
For 'Sunrise to sunset' use 'daytime'
For some random consecutive period of 24 hours, use '24 hours'
For midnight to midnight (24 hours) use 'calendar day'.

It is not that English is ambiguous, it is that so few people choose to use the correct words to give the specific meaning they intend to convey.
The diversity of the English language allows you to choose exactly the right word(s) to convey your meaning clearly, but is lost on those who believe that any word can simply be replaced by any other which appears under the same heading in a thesaurus.