Matt has explained the four stages very well, and those are in line with PDCA cycle. And for any organization it is not mandatory to get all four stages covered by the same vendor. It could for example be vendor 1 for stage 1 and 2, vendor 2 for stage 3 and vendor 4 for the last stage. One has to be very careful in Discovery phase, to chalk out the exact requirements neatly, clearly and crisply as the whole success of the project (all phases) is depending on this phase. I will prefer to go for an extra cushion always for any organization in Discovery phase. If the requirement is x no. of network points, go for 10% extra to cater to hidden needs in future.
All phases should have a perfect way of verification at individual phase completion as these phases are going to happen in a waterfall manner.