A maximum score is a per-hole limit on strokes that your league's committee can choose to set as its format. Net double bogey is a separate cap that applies when your round counts toward a handicap. Your league decides whether it plays with a maximum, and the handicap cap applies either way.
What is a maximum score format?
It is a form of stroke play where your score on a hole is capped at a number the committee sets, such as twice par, a fixed number, or net double bogey. Once you reach it you can stop playing the hole, and you record the cap if you haven't holed out. Picking up at the limit is encouraged to keep play moving. Whether your league does this is up to the committee, so ask the organizer. See Rule 21.2.
What is net double bogey?
It is the most any hole can count toward your handicap: par plus two strokes, plus any handicap strokes you get on that hole. If you score more, your handicap uses the capped number. Before you have an established index, the cap is par plus five on every hole. See Rule 3 of the Rules of Handicapping.
Does this change the score on my card?
Not by itself. The cap changes how a round is treated for handicap purposes, not what you wrote down. In a league with computed handicaps, the League Index applies the cap to your posted rounds for you, so you don't adjust scores by hand. For how your index and net score work, read Understanding your handicap and net score.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.