Project Management deals with the management of a specific project, which has a commence date, a number of tasks and a completion date. This is further explained as the management of a specific project. A Project Manager would typically oversee the delivering of projects on time, assigning tasks to developers and designers and ensuring client satisfaction.
Operations Management refers to the ongoing management of daily works of a company, such as technical support, network management, etc. With Operations Management, there is no set end point. An Operations Manager would typically be involved in all operations of a company, ensuring that everything is running smoothly and that staff are delivering correctly.
Let's look at an example - A web agency may have many projects running at the same time and once these projects are deployed, the project is finished, in terms of operations management, the operations manager is still occupied with the day to day support and management of the deployed project, ensuring that it is still running correctly, fixing various problems and so forth