The VMware Tools package that ships with VMware products contains both open source and closed source components. The Open VM Tools packages is just the open source subset of the VMware Tools package. In general, you can expect that Open VM Tools will provide the same basic features that VMware Tools does, but there may be a few extra things that VMware Tools includes. Also, if your Linux distro has a VMware Tools package in it's repositories, it is based on Open VM Tools an not VMware Tools.
UPDATE: Earlier I was reluctant to be specific about what code was in open-vm-tools vs VMware Tools because the set changes. That's still true, but I found a list from the open-vm-tools website, so I though I would include that here.
The open-vm-tools FAQ says the following about what code it contains vs VMWare Tools:
All of the non-experimental kernel modules and user level applications
that have been developed solely by VMware are being released. Certain
experimental drivers are planned for future release. VMware will
encourage 3rd parties to release their contributions under the GPL.
- Drivers for devices and filesystems access
- Memory ballooning
- Shared folders
- Drag and Drop, Text and File Copy/Paste
- Clipboard sharing
- Disk wiping and shrinking
- Time synchronization
- Automatic guest screen resolution resizing
- GuestInfo (provides statistics about guest environment)
- Guest SDK (provides information about the VM)
- Soft power operations
- Multiple monitor support
- GTK Toolbox UI
Again, this set changes over time. As new functionality is released via VMware Tools, it may take some time for it to find it's way to open-vm-tools, or it may not make it there at all if VMware is unable to release it.