Wikipedia's article on Ohm actually covers this!

http://en.wikipedia.org/wiki/Ohm#Ohm_symbol

"Unicode encodes the symbol as U+2126 Ω ohm sign, distinct from Greek omega among letterlike symbols, but it is only included for backwards compatibility and the Greek uppercase omega character U+03A9 Ω greek capital letter omega (HTML: Ω Ω) is preferred."

And from the Unicode Standards doc that is the source for that section:

"Greek Letters as Symbols: The use of Greek letters for mathematical variables and operators is well established. Characters from the Greek block may be used for these symbols.

For compatibility purposes, a few Greek letters are separately encoded as symbols in other character blocks. Examples include U+00B5 µ n the Latin-1 Supplement character block and U+2126 Ω in the Letterlike Symbols character block. The ohm sign is canonically equivalent to the capital omega, and normalization would remove any distinction. Its use is therefore discouraged in favor of capital omega. The same equivalence does not exist between micro sign and mu, and use of either character as micro sign is common; for Greek text, only the mu should be used."

Is there a separate symbol for A?

Unicode has lots of characters that look alike, because, well, lots of human languages ended up with similar-looking characters.

Even English speakers will easily confuse 1,I, and l, depending on how they're represented by the browser. And 0/O.

For more fun, try drawing any shape on http://shapecatcher.com/ and see all the similar-looking Unicode characters.

This is a really fun way to explore unicode, thanks.

Because one is a greek letter, and the other is a unit of resistance. The fact that they're represented by the same symbol is irrelevant.

If that were the case, we'd need separate codepoints for every letter used as a unit of measurement, from A for ampere onwards. In fact, it's just there for legacy reasons, as pointed out elsewhere: the convention for units of measurement is to use normal letters, regardless of whether those are Latin or Greek.

Why does HTML have a <strong> and a <b> tag?

<strong> is emphasis/semantic and <b> is visual/style.

The parent was asking a rhetorical question, and drawing an analogy between the two: omega and ohm have different meanings, therefore it might be useful to be able to distinguish between the two. (Note that I say 'might'; when it comes to a character set, I'm not sure I 100% agree ...)

Because they have rather different meanings. Capital omega (Ω, U+03A9) is a Greek letter, with the lower-case form ω; ohm (Ω, U+2126) is a symbol used in electrical engineering with a related symbol "mho" (℧, U+2127).

FYI, that all units measuring physical properties named after scientists use capitalized letters for their abbreviation[1]. So the ohm (named after Georg Ohm) is abbreviated as the uppercase omega, no idea why they are different unicode values, since they do not have different meanings.

Note that omega was probably used so that the 'O' wouldn't be confused with '0', e.g. 4O would be confusing, but 4Ω is not.

[1]The tesla is abbreviated 'T', joule is 'J', etc. etc.

Using the Ohm symbol is actually discouraged. The only reason it's there is for round trip conversion to other character sets.