I am not an AIX admin, but Tar and Dump are reasonably alike across UNIXes.

Tar (the Tape ARchiver) was originally meant for writing multiple files to tape. By specifying a file as an output device, it can store several files in a single file (sometimes referred to as a 'tarball').
By compressing the resulting tarball with GZip, several files can be combined into a single, compressed archive.

Dump usually 'dumps' (backs up) the contents of a filesystem to a 'dumpfile'.
This means that all files included in the filesystem are included in the resulting dumpfile. Generally, an entire filesystem is restored in a single 'restore' command.
There are other ways to use dump (HP-UX has a wrapper script named fbackup), where dump performs (incremental) backups of sets of files.


The 'regular' version of tar, dump and restore are usually supplied with any UNIX distribution.
There is a GNU version of Tar that can perform in-line compression, incremental backups and other useful functions.