This is always a controversial issue. If you use PostScript fonts, then yes, they should appear in the font menu, including any variation you might have installed. TrueType, on the other hand, maybe not.
When you specify, say, 'Gill Sans Bold' in the font menu, there can be no argument about what that is. If your file is opened on a Mac without that font, a warning is issued.
If you specify 'Gill Sans' and use the character buttons to make it bold, then things become a little confused. Quark will substitute it for 'Gill Sans Bold' if it's available, and if not, it will try to render a bold version of the font. Usually, it doesn't look that good, and if the standard version is all that's available on another computer, it may display differently without giving a warning.
Now back to TrueType fonts. There may be a bold version and the only way to access may be to use those charactor buttons. Again, if your printer's computer doesn't have the full set, it may try to create it's own version with unpredictable results.
To be safe, you should use Type 1 wherever possible, and avoid those buttons. Although TrueType fonts aren't as bad as some purists would make out, and will usually print ok, this is one situation that may cause problems.