New software is often numbered, such as GroupWise 5.4
Is the number to the left of the decimal called the version, and the number to the right the release? That is, going from 5.4 to 5.5 is not upgrading to a new version, it is just upgrading to a new release, right? And is going from 4.x to 5.x a version upgrade?
It completely depends on the software manufacturer. Where I work, incremental releases are usually the number after the dot, and are free upgrades. However, I believe we’re coming out with a 1.5 version that we are charging for. I don’t think the industry in general has any guidelines for such things.
At a retail software shop where I used to work we would basically follow the same scheme that Athena’s employer does. Numbers to the left of the dot were major revisions and represented massive changes and new functionality. Numbers to the right of the dot were more minor, usually bug fixes. If you changed or added a number two places to the right of the dot you were making really minor changes.
This was all decided arbitrarily. At one point we changed numbers to the right because we broke the software into two separate packages and although the functionality did not change, the way it was sold and quite a bit of code changed. Basically the numbers used were decided by marketing.
I think it is generally accepted that the bigger the change in number the bigger the differences are between the previous and the current version.
The numbers are indeed arbitrary. Originally, you put out a 1.0 version as your first full version. Any bug fixes might be 1.01, etc. A more major fix might be 1.1, etc. The next upgraded version would be 2.0, etc.
That scheme was abandoned for a lot of reasons:
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People learned not to trust version 1.0 and would wait for 2.0 to come out before they bought it.
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Sometimes competition required skipping numbers. WordPerfect used the standard numbering. Microsoft Word skipped versions 3, 4, and 5 so that they could put out Word 6.0 at the same time WordPerfect 6.0 was coming out.
Now, if there is a number, they use whole numbers only in their marketing, no matter what the in-house numbering is. Microsoft has switched totally to a year of issue scheme, so the versions of Word are 1.0, 2.0, 6.0, 6.0 with Win95, 97, and 2000.
Most FSF and related software (GIMP, or the linux kernel, for example) seem to follow a scheme of:
X.x.x - X represents major release
x.X.x - odd, unstable release, even, stable release
x.x.X - updates, minor changes, patches, etc.
MOST software these days has a three part version number, i.e. x.x.x. It’s different depending on the software and manufacturer. The Linux kernel, for example, the first number is the major release, then the minor release, then the really minor release. It takes a LOT of change to come up with a new major release. Kernel 2.0.0 had a lot of code totally rewritten and was the first kernel to include low-level support for non-Intel architectures. It’s taken about seven months to get from 2.2.0 to 2.4.0 (odd numbers in the minor release are “development” versions). Generally, really minor releases are made every month or so.
Apple follows a similar verison scheme, and so does Adobe.
A very minor quibble:
Word 97 (Office 97) was Word 8, and Word 2000 (Office 2000) was Word 9. I have no idea what happened to 7.
The non-year numbers are useful in-house and for beta testing, if the “official” name hasn’t been released. Although with the year scheme, it doesn’t take a lot of guesswork to figure out the official name. 
System: Microsoft Windows 2000
5.00.2195
Microsoft Internet Explorer
Version: 5.50.4134.0600
Apparently Microsoft uses a modified x.x.x system, retaining the traditional major.minor nomenclature and appending the software build number as the third group of digits. Thus, I see that my system version is 5.00, build 2195, but what is the fourth set of digits (0600) in the IE version?