I have burgues and some of the others...
Those special swirly letters are alternates of the regular letters. Opentype fonts have alternates for lots of characters, and you can access these characters by going to the glyphs pallette in your design program. Check out this page for some interesting info on how much work goes into making all those alternates:
http://blog.parachutefonts.com/?p=16
Some design programs handle this well and other ones don't handle it at all. The later adobe ones tend to substitute the prettier letters automatically, and to connect ligatures (two letters that can be drawn as one special character, like "tt") automatically. Like try typing it in photoshop, and I bet at least some of the letters change. If you do it in illustrator, you can get to any special letter by going to the type menu and finding "glyphs". I think the process is similar in indesign. But other programs like flexi don't bother with it at all. Kind of lame.
Some of the cheaper fonts that don't use the opentype (.otf) file format will fake it by making the special ligatures and alternates accessible by typing alt codes. If you're in windows you can figure these codes out by doing start --> run --> charmap, click ok, find the font you want, go to "Group by" at the bottom and do "unicode subrange". Then from the popup window scroll the bottom for "private use area" and they'll usually be there. Click on one to highlight it and see the alt code for it.
Other fonts like championscript will include a 2nd font that just has alternate letters.