VPN vs. Remote Access

It's been some time since I've setup a Hamachi VPN for a client, but alas it looks like we're about to go down this road again.  However, what is becoming clear to me is that some users are unclear as to the differences b/w using a VPN vs. a remote solution like TeamViewer or LogMeIn. Without getting into the techno-babble, let me draw a clear distinction: When using a VPN, you are doing your work on your VPN-enabled device while accessing the data within the network, but most likely it resides on a different device. In contrast, when using a remote solution like TeamViewer or LogMeIn, you are running a program on your device which takes remote control of a PC in the office, which by design has access to resources. Was that clear?