Apple is now officially bigger than Microsoft. But only on paper.

This week marked the first time the market capitalization of Apple ($221 billion at the close of trading last night) exceeded that of Microsoft ($219 billion). Market capitalization is the paper value of the company: the number of shares multiplied by the current market price.

In terms of the business they do, Microsoft remains much stronger: $20.4 billion pre-tax profits from $58.4 billion revenue, compared with Apple’s $11.7 billion profits from $42.9 billion revenue.

But momentum is certainly with Apple. As Information Week notes, when Ballmer took over Microsoft in 2000, its market capitalization of $556 billion absolutely dwarfed Apple’s $15.6 billion.

While it’s difficult if not impossible to read what investors as a whole are thinking when they carry out the buying and selling which determines stock prices, there seems to be a clear overall message: they acknowledge Microsoft still dominates the market for full-blown computing software, while Apple does a much better job than Microsoft when it comes to the markets for other devices. Just compare the success of the iPod, iPhone, or iPad to the poorly-received Zune, a ludicrously delayed Windows Phone 7 series, and a combination of a non-existent Courier and a collection of independent manufacturers who appear to be getting cold feet about relying on Windows for their tablets.