TTF are Windows-based fonts, like Arial and Times New Roman, and must be installed on your computer (in C:\Windows\Fonts for Windows XP) before AutoCAD will recognize them. Plotting weight of TTF fonts is controlled by "bold" options, if available.
SHX fonts are shape-based, and only have to be put in a support file that AutoCAD searches in order to display properly. Unlike TTF's, their plotting weight depends on the color of the text (with CTB plotting) or the plot style (with STB plotting).
You should always check with your clients & consultants to make sure everyone has all the fonts they need -- some have special characters that don't display properly if you substitute a different font.