Work orders are reserved for simple non-IT tasks. The workflow of a WO is very simple. Changes, otherwise, implement all ITIL recommendations for change management. That means, approvals and a lot of other stuff.
But for user request the best module is service request management. Service Requests can be configured to need approval. And if aproved it launches a process where changes, work orders or incidents can be created.
For instance: Yo can create a service request called: "New job place"
This service request needs to be approved by the HR manager. If approved it launches a Work Order to the maintenance deparment to send the required furniture if needed. Also creates a change to add the user to the active directory. And finally creates a change to prepare a new PC.
Work Orders are not just for non IT Tasks, they can be used for "anything" including IT related requests.
Work Order Management is included with SRM as SRM can be installed as a standalone application not requiring ITSM. SRM requires a fulfilment application, and this is why Work Order Management is provided with this application.
Work Order Management implements other AR functionality including Task Management and can be seen as a "cut down" version of Incident Management. Hence, you can have an IT system based purely on SRM if applicable. Most companies have both ITSM and SRM, but it is worth knowing that SRM can be standalone.
If you have both ITSM and SRM, then you can leverage Work Order Management, Incident Management and Work Order Management which allows for a large scope of activities.
For the example you have provided, you can handle this in a number of ways dependant on where the approvals are needed and how well your business is at implementing ITIL recommendations.
As Jose has mentioned, you have a level/s of approval Management, Level, mixture (dependant on SRM version) in SRM "before" the request is created in the fulfilment application (Change, Incident, Work Order). Dependant on how complex the approval process needs to be, you can then extend the approvals into Change Management.
By definition (ITIL), if you are tracking Software then this "would" be a Change request - but there is no reason why you could not use Work Order Management if your business is not that ITIL mature in implementing your processes. You have the addition of Task Managment in Work Orders as well, so it is a quite useful module.
Some customers I know use Task Management in Work Orders to track approvals as well as Change Management is quite a complex application and they do not need the "extra" functionality and just want to track the approval request.
So in summary, the business can drive the decision on where to handle the request based on processes, ITIL maturity, etc.