A virtual private network (VPN) is a secure remote connection that allow a user to access a server and access a remote device. The server listen at tcp port 5900 and users must be authenticated to gain access to a remote machine.
A direct access user must be on a VPN for remote access to possible on another device.
A Network Intrusion Detection System as the name suggests it "detects" the attackers / vulnerabilities existed in the network system / infrastructure.
A Network Intrusion Prevention Detection System as the name suggests it "prevents" the attackers from hacking the system. While a detection just detects the abnormalities where as a prevention system can prevent them.
The detection system detects the vulnerabilities, security threats and the attackers in the system through the web traffic analyzers and security analyzers.
The prevention system prevents the network from being compromised. It tries to regain the access if already compromised.
Both the NIDS and NIPS have to be coordinated for the full protection of the network.