Technical or Business Engagement of a Service Provider
This is a concept often overlooked in service provisioning but one that is important to consider, even if it is only a high level concept. There are two basic "places" where a service provider can be engaged. One is "as IT" and one is "by IT."
By this, I mean that in one case customer management brings in a service provider whose interface to the business is a business interface (e.g. the SP is the entire IT department and reports to the business as any department would, technical details are kept inside the SP / department, it's a business discussion only from the SP to management.) In this world the "CIO" role is inside of the service provider and, ideally, would have a seat at the decision table for the customer's business in a broad sense. [The service provider could, of course, oversee other service providers or even internal staff.]
The other approach is for the customer to have their own IT "head" that oversees the service provider and, may, also oversee internal staff or other service providers. In this case the interface between the service provider and the business is a technical one, like a team reporting to their department rather than a department reporting to the business.
The differences between these two approaches can be relatively important. The differences are around responsibility and opportunity. In the case where the SP reports to the business directly, it is solely up to the SP (within the bounds allowed it by the customer) to do a good job. Proposals, management, teamwork, documentation is all clearly for the SP to handle. The SP is responsible for "selling" IT to the business and showing value.
In the other case the SP is just part of the IT department and could easily be curtailed or micromanagement by the IT management of the customer and be forced to do things that they do not feel are appropriate, safe or financially sound. But as they are not reporting to the business, it is not their place to report this. This creates a potential conflict of interest and requires critical professionals to either avoid reporting concerns to the business or is forced to skirt their command chain to do so. The SP has a conflict in wanting to support the department that pays them, but also has a duty to the company that they report to. Often the perception of the value of the SP is defined by IT management, not the performance of the SP so the SP is often forced to placate their managers even to the detriment of the customer.
Neither situation is perfect or always clear, but understanding that these two modes exist and can heavily impact how service providers function, whether they succeed and how the business views them is critical.
As with most things, it is almost important to note that no one controls this arrangement except for the customer. The SP has no say in the matter other than to simply refuse paying work that does not fit ideal situations.