Consider this MWE:
\documentclass{minimal}
\usepackage{fontspec}
\setmainfont{Latin Modern Roman}
\setsansfont{Latin Modern Sans}
\setmonofont{Latin Modern Mono}
\begin{document}
X marks the spot.
\end{document}
Using the standard ISO of TeXLive 2014 on Ubuntu 14.04.1, LuaLaTex compiles this; XeLaTeX, on the other hand, gives this error:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! fontspec error: "font-not-found"
!
! The font "Latin Modern Roman" cannot be found.
!
! See the fontspec documentation for further information.
!
! For immediate help type H <return>.
!...............................................
l.4 \setmainfont{Latin Modern Roman}
What’s going on, and how do I fix this?