In Waterdeep: Dragon Heist, there is an encounter with an apprentice wizard.

Apprentice Wizard in the appendix has a stat block with a spell list, however the adventure text states that this apprentice wizard has a spell book with a spell list that contains more spells than the stat block.

I'm happy running it with either set based on what my players can handle and most importantly, what will serve the game we agree we want best, but which spell list is intended to be used?

The following is an excerpt from the apprentice wizard stat block (emphasis mine):

Spellcasting. The apprentice is a 1st-level spellcaster. Its spellcasting ability is Intelligence (spell save DC 12, +4 to hit with spell attacks). It has the following wizard spells prepared:

I would take this to mean that while this apprentice may have more spells in his spell book, he has a certain set of spells prepared. If you decide he can swap out these spells (as if he were a "player character" wizard) that is within your power as DM.

Apprentice Wizard can use spells in the spellbook

Stat block spells are in the spellbook

As an introductory statement: all published adventures use the MM as a reference¹.

Most monsters are referred to in bold text: that means "go to the MM and see what that monster has." All other monsters will be in the Appendix for the adventure; each published adventure I have indicates which are in an appendix.

With that in mind, the Monster Manual (page 10, under "Spellcasting") says:

The monster has a list of spells known or prepared from a specific
class. {snip}

You can change the spells that a monster knows or has prepared, replacing any spell on its spell list with a spell of the same level and from the same class list. If you do so, you might cause the monster to be a greater or lesser threat than suggested by its challenge rating.

In this case, the CR won't change; they are all 1st level spells, and I'll argue that the three in the stat block are the best choices to be prepared when the PCs are encountered.

Apprentice Wizard is not in the MM. It is in Volo's Guide to Monsters. The stat block in this adventure's Appendix (p. 194) is identical to the one in Volo's Guide (p. 209).

The spells available to that NPC (a first level caster) are (1) those from the stat block, which are all in the spell book:
burning hands, shield, disguise self

and (2) some other spells

false life, unseen servant, witch bolt are the other three spells listed in the spellbook under the "Treasure" section for the encounter; he carries the book in his satchel (p. 29)

Simple Solution

He has the stat block spells prepared by default. Makes perfect sense, each is a useful spell: Burning hands, Shield, Disguise Self. Going with that makes it easier on the DM.

Tailored Solution

Replace one or all of the ones prepared (per stat block) with spells from the book that is available to that NPC wizard. Put another way, this is an NPC wizard with a little "fleshing out" already done for the DM.

• My brother and I both do the same thing in our campaign. For Mage
  and Apprentice wizard NPC's, we usually create a spell book and roll
  randomly to see which ones are prepared that day before the session
  starts. (Some old school habits die hard)

Which do you prefer: simple or tailored? Go with that.

The published adventure does not limit you to the ones in the stat block.

¹ On page 7 of that adventure is a section entitled "running the adventure" which states that you need the Player's Handbook, the Dungeon Master's Guide, and the Monster Manual to run this adventure. These are core rule books for the adventure. (SCAG is "helpful, but not necessary," they say).

Wizards can know more spells than they can prepare

It's likely that this NPC wizard's spell book contains more spells that his stat block because those in his stat block are those he has prepared for the day.

Spellcasting. The apprentice is a 1st-level spellcaster. Its spellcasting ability is Intelligence (spell save DC 12, +4 to hit with spell attacks). It has the following wizard spells prepared:

As a first level spellcaster, he should have the same number of cantrips as a Wizard PC at that level (3 cantrips; PHB, pg. 113) and either six or eight spells, depending on whether he's equivalent to a level 1 or level 2 PC (see PHB, pg. 114 for starting spells from spellbook):

Spellbook

At 1st level, you have a spell book containing six 1st level spells of your choice...

[...]

Learning Spells of 1st Level and Higher

Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook.

If the NPC was built with PC character creation rules, then using the Wizard class features would have come to the same conclusion.

Other published adventures have also had wizard NPCs whose spellbook you can find, and which contains more spells that in the NPC's statblock, but I am away from my books so currently so I can't provide any specific examples.