I spent five years in this space (in a small consultancy that was acquired by GlobalLogic last year). I think this is how one of our salespeople might describe the process.

The reality tends to be somewhat messier. I especially disagree with the "personal chef" analogy. A personal chef is an expensive, dedicated, long-term employee - much closer to a full time SWE than to a consultancy. It's more like hiring a catering company for a wedding.