Not even close - sweet onions (like Texas 1015s, Vidalias, or Mauis) may be whitish, but they have noticeably more sugar embedded into the structure/tissues of the onion itself. Sweet onions are not white (or yellow) onions, or vice versa. FWIW, Vidalias are a bit less crisp than the others, which helps if you're really after carmelizing, but I find 1015s are the "sweet spot", so to speak, of softenability and enough fiber to hold up so they don't turn to mush.
Red onions are a different flavor profile altogether, and best for some (not all!) Mediterranean or Mexican dishes, or smoked salmon (NOT lox - yuck!) on a bagel with cream cheese and capers.
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Yellow onions have a stronger flavor, even after cooking. (Though cooking of course lessen it a lot.)
White and sweet are essentially the same, with the latter being slightly sweeter.
In the end they do taste similar cooked. Biggest difference is price. Yellow is usually 20% cheaper than white and 40% cheaper than sweet.