Kind of. pack 1's typically have 3 different kinds of cards. Let's call them card #1, 2 and 3.
Pack 2's typically have 3 cards as well, 1 or 2 of which are likely duplicates of the same card you get in pack 1. So cards 3-5 or 2-4.
Pack 3's always have only 1 unique card, and 2 (or is it 3? I think it's 2) duplicates that you could have gotten from packs 1 and 2. And pack 4's have nothing new except for unison spellcards (most of which don't seem very useful IMO, and most of the time you'll simply get cards you could have gotten from previous packs), exceptions are Reimu with Fantasy heaven, and Aya with Coercive reporting..
Every character starts with 3 spells, MOST of the time these are 2 spells which you can get from pack 1s, and one that you cannot get from pack 1, but can from pack 2. However some characters start with nothing but spells you can from pack 1's.
An example of Marisa:
Pack1: May contain her +sp% buff, Galaxy locus, or Starlight ray (or whatever it's called)
Pack2: May contain her +damage buff, galaxy locus, or Master spark.
pack3: May contain +damage buff, Starlight ray/sp buff (I think), and Mega master spark.
pack4: May contain some cards from the above, but if you're lucky, Master spark EX(U), or Witch's banquet.(U).