5e: Basic spell question

This may be a simple question, but please help.



Wizard spells: PH says you start with a spell book that has six first level spells.



But in the chart on p 113, it says a 1st level wiz has two 1st level spell slots.



On p 114, it says ( I am paraphrasing a bit) " prepare the list of wiz spells available for you to cast . . . Choose # of wiz spells from your spell book equal to int mod + wiz level. Spells must be of levels that you have slots.



Ex: 3rd level: four first and two second level slots. With an int of 16 gives six spells of 1st or 2nd in ANY combo chosen from spell book."



So, if I have 1st level wiz with 16 int, I can cast four spells a day ( not including cantrips), right? If that is true, what is the difference between having 6 spells from spellbook and 2 spells on the spell slot chart on p 113 and being able to cast 1 spell+int mod before long rest?



I know the answer is simple, but I just can't see it. Help, please. Thanks.

5e: Basic spell question