Does Ubuntu provide extra fonts through a font package?

Yes.

In a terminal...

apt-cache search font

will yield all results. Or...

apt-cache search font | grep ttf

will yield a list of TrueType fonts. You could save the output to a file to examine it:

apt-cache search font | grep ttf > ttf_font_packages

If you wanted 465 free TTF fonts in the ttf-aenigma package and the tuffy font after reading the output, then:

sudo apt-get install ttf-aenigma fonts-tuffy

Aside from packages, you can create a directory for your own fonts.

cd
mkdir .fonts

Then, drop as many fonts as you like into that directory (~/.fonts). You've also got some graphical software selection tools available if you do not like the terminal.

Yes, you can have Windows TrueType fonts through Ubuntu Restricted Extras (Package that installs beyond fonts, flash, java and audio and video codecs) and TrueType Microsoft fonts Installer, to get them type the following in the terminal:

sudo apt-get install ubuntu-restricted-extras ttf-mscorefonts-installer

Perhaps a bit extreme, is this attempt to install all fonts:

sudo apt-cache search ^fonts- | sed 's/^\(fonts-[^ ]*\).*$/\1/' | xargs sudo apt-get install

I think the best option is to use the Synaptic or any other package manager and the section fonts from (universe) for example.