Hi Zandra,
In addition to Harry's excellent definition for "manage" vs "control" quality, I will share a couple of other examples to hopefully illustrate in a different context.
1. In manufacturing, the use of "poka yoke" (fool-proofing methods) during assembly process would be considered an example of "managing" quality - i.e.: by preventing errors in the assembly process, the organization can eliminate the losses that will arise from assembling a subassembly incorrectly, only to detect it during the "control" process of inspection.
Detecting defects at the "Control" stage is usually more expensive to the organization, since it means the materials and resources have already been expended in
creating a "defect" which is not fit for purpose - which must either be reworked or scrapped.
2. In software, "manage" quality would include methods like peer-review of code, pair programming, etc. to ensure code gets reviewed at the development stage, before handoff to the testing teams.
An example of "controlling" quality would be detecting bugs during QA testing which is costlier than during development.