What is the difference between these two versions? When the installer is run for 3.8 beta 2 the version number displayed is 3.7.2?

Our network team do not want to have this software available for use if it is considered a beta version.

They are the same release. Because of how Eclipse's update mechanism works, in order for it to pickup an update, the version number has to be higher than the current version... so in order for us to label our Beta builds greater than the current stable release (3.7.000) but less than the final release (3.8.000) we end up using increments of the previous major release for our betas.

We are hoping to release 3.8 GA later this week or the beginning of next week, so you might want to wait for that.