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Name of the Project lifecycle without full lifecycle

In our company, we have projects following from Customer Requirement with meeting up to Product delivery with training and documents as the full life cycle.

But for some projects, we are doing 'Task-Based works'. That is, the customer asks us to do only part of the life-cycle ... the remaining work is taken care of by them. For example, Product development has done by them but they send the result to us for Testing. As another example, we will do only Functional design specification and initial configuration. Like this, we are having some projects mostly billing as per the time sheets rather than a lump-sum price.

So, under which method do such kind of projects fall? Some referred to this as the Agile methodology. Is that correct? If not, then what is the correct terminology for such works? Currently, we are referring to them as 'Task-Based Projects'.