Unicode is opposed to Western (ISO Latin 1), Arabic (ISO-8859-6), etc. These are text encoding languages. In Safari, Edit > Text Encodings will display a list of these.
OpenType is neither PostScript nor TrueType. These are Font formats, or page description languages.
Unicode is a style of text encoding. It's a kind of universal alphabet. To get a sense of what that means, try the following (it's fun!). From Mellel, go into Edit > Special Characters. In the character palette, select View: Code Tables from the dropdown menu at the top.
Click around. As you scroll through all the, say, Cherokee glyphs, you can see in on the left the numbers 000013A0, sometimes represented 0x13A0 (in decimal numbers, that represents 5024). Cherokee fills six rows of 16 glyphs in the Unicode table, 0x13A0 through 0x13F0. The Canadian Aboriginal Syllabics start on the next row 0x1400
Basically, Unicode-8 applies an eight digit hexadecimal number (numbers represented not with the ten digits 0-9, but the sixteen "digits" 0123456789ABCDEF) to each glyph used in any human writing system. Since there are 4,294,967,296 eight digit hexadecimal numbers, that's more than enough.
When someone says "Unicode font," it's not really a font format they're talking about. It's simply a font (of any format) that contains glyphs for many or (rarely) all of those different languages. Several of the fonts that ship with OS X are in this category. Lucida Grande is one. It is, as you can imagine, quite an undertaking to put one of these together.
TrueType, the older PostScript, and the newer OpenType are font formats, or more properly "Page Description" languages used to communicate with printers. PostScript, designed by Apple and Adobe in the 80s, pretty much got desktop publishing started as a thing, and is still used by many laser printers and the odd artisanal type foundry. There are three "types" of PostScript fonts, type 1, type 2, and well, type 3, but I don't know the difference off the top of my head. If you want, you can make a PostScript page description file under the PDF button-menu thing in Tiger's standard print dialog box. UNIX users sometimes use PostScript files the way normal people use PDFs (needless jab).
TrueType is a codevelopment of Microsoft and Apple, from the mid-90s, I think, and it modernized PostScript for new kinds of printers, but didn't really improve it typographically speaking. Actually because TrueType allows all kinds of crazy transformations to type (fake small caps, fake bold), the kind of thing people did a lot of on the web in the 90s, type purists regard it with (justifiable) suspicion.
OpenType is the new one, the digital type world's attempt to be everything to everybody. It has a whole slew of features, and a full featured OpenType font in a full featured OpenType application (pretty much only Adobe InDesign) can do amazing things. Beyond the features Mellel makes available, some of the fonts have alternate glyphs for certain letters and numbers. Check this out (Adobe's site).