Haah..... When so many people search Google for this, well I thought it wouldn't harm to write a note on this basic concept.
"Not for Pros".
NMS - Network Management System
EMS - Element Management System
Well, lets define what is a network Node. A node is a single device or entity usually a single physical box, such as a computer, server, router, switch, etc. The node, usually is connected to other nodes in the network, interacting and exchanging data in the language the local network devices understand.
Of course a Network, is a bunch of interconnected nodes where communication between them is usually possible at will if any device wants to talk to other devices.
EMS is a system which manages a single Node or group of similar Nodes. The word 'Element' refers to a node in a network.
NMS is a system which manages the entire network or multiple networks.
EMS can sit in one part of the network and manage node/nodes in other part of the same network(or a different network) or it can sit inside the managed device itself and extend management interface to the outside world.
NMS can sit inside the network or outside the network (but can reach the network) monitoring all the nodes in the network or most of the nodes in the network and the connections among them.
So, the main difference between EMS and NMS is the ability of NMS to understand the inter-relation between the devices of the network. An EMS does not understand the communication links or relationships between devices. It only knows the intricacies of a single device, though it can manage multiple devices of similar type, it treats all the nodes in that group as independent devices not recognizing how they interact among themselves or their complementing functionality or what they mean to each other.
Another functionality of NMS which differentiates it from EMS is, its ability to monitor the inter-links among the devices, or the connecting links in the entire network or the ability to report the faults occurring at various nodes in the network and also predict how such faults disrupt the communication links in the network causing the whole network to not function or malfunction.
So, one can roughly say,
NMS = EMS + Link/Connectivity Management + Management of Relationships among devices + Understanding of contributions of each node in the functioning of the network itself
How does NMS or EMS look like?
Well, both of them can be just softwares with/without graphical interface running in a separate server or in a normal desktop computer or in a network node/device (usually EMS, with a web server).
Current trend is, a server with GUI developed in java or with a web server or an enterprise server.
NMS can perform very complex operations with respect to the network as a whole. The functions are termed as FCAPS.
Fault - Report Link Failures and node failures or faults in the part of a device
Configuration - Modify/enable functionality of a device/node
Accounting - Perform billing, accounting related functions for a commercially used business network
Performance - Measure/improve performance or utilization of the network or devices
Security - Protect the devices or network from harmful or illegal access, implement hierarchical access policy within the network, provide user management (human users accounts) in conjunction with device/network/service access
Literally an NMS can do anything with the network if anyone is willing to put such functionality in the NMS. It can create, maintain, provision or destroy a network or a device within the network. From sending an electronic message to operating a robotic arm to mechanically connect or disconnect devices, to showing the mobile users and their movements on a screen to shutting a water pipe or door, or closing a dam, to anything. The possibilities are endless.
But the devices in that network should be designed in such a way that an NMS can manipulate them easily.
The last notable capability of an NMS is to manage dissimilar devices that is differing in functionality, differing by vendor, or differing in its basic nature (the language a device understands, e.g. IP device and Telecom Device).