According to Agile practices and way-of-working there are no projects. Instead Agile is based on the assumption of a regular, steady cadence of work being applied to a product. The work intended is outlined on a backlog and after each Sprint the output is validated and considered while planning the next Sprint. This is very similar to old-school maintenance approaches given that the execution of work is different.
A traditional project sets out what to build in a specification and resources are allocated according to estimations of what is needed. In Agile it is the other way around where the resources are fixed and the specification is ever changing reflect what the team(s) accomplish in each Sprint. Hence the traditional Project concept is not relevant, instead it is more appropriate to talk about an Engagement where available resources are utilized under a set period of time.
Using the same word with multiple meanings are never a good thing!
Therefore, I suggest using the term Project when offering to build a solution with a fixed specification and moving capacity. When you have a situation where you offer a fixed capacity and a moving specification it should be called an Engagement.