What is the difference between /tmp and /var/tmp?

/tmp is meant as fast (possibly small) storage with a short lifetime. Many systems clean /tmp very fast - on some systems it is even mounted as RAM-disk. /var/tmp is normally located on a physical disk, is larger and can hold temporary files for a longer time. Some systems also clean /var/tmp, but less often.

Also note that /var/tmp might not be available in the early boot-process, as /var and/or /var/tmp may be mountpoints. Thus it is a little bit comparable to the difference between /bin and /usr/bin. The first is available during early boot - the latter after the system has mounted everything. So most boot-scripts will use /tmp and not /var/tmp for temporary files.

Another (upcoming) location on Linux for temporary files is /dev/shm.

/tmp may be, and sometimes is, cleaned on reboot. /var/tmp is preserved between reboots.

See the Wikipedia article on the FHS.

POSIX Base Specifications, Issue 7 on /tmp:

The following directory shall exist on conforming systems and shall be used as described:

/tmp

A directory made available for applications that need a place to create temporary files. Applications shall be allowed to create files in this directory, but shall not assume that such files are preserved between invocations of the application.

The File Hierarchy Standard 2.3 on /tmp:

The /tmp directory must be made available for programs that require temporary files.

Programs must not assume that any files or directories in /tmp are preserved between invocations of the program.

Rationale

IEEE standard P1003.2 (POSIX, part 2) makes requirements that are similar to the above section.

Although data stored in /tmp may be deleted in a site-specific manner, it is recommended that files and directories located in /tmp be deleted whenever the system is booted.

FHS added this recommendation on the basis of historical precedent and common practice, but did not make it a requirement because system administration is not within the scope of this standard.

POSIX does not specify /var/tmp. The FHS does though:

The /var/tmp directory is made available for programs that require temporary files or directories that are preserved between system reboots. Therefore, data stored in /var/tmp is more persistent than data in /tmp.

Files and directories located in /var/tmp must not be deleted when the system is booted. Although data stored in /var/tmp is typically deleted in a site-specific manner, it is recommended that deletions occur at a less frequent interval than /tmp.