State of being vs forms of desu


This might come across as a dumb question, but learning through multiple
websites for basic grammar, I started with stuff like
[this](http://www.guidetojapanese.org/learn/grammar/stateofbeing). After
learning a bit more about verbs conjugation, I've gotten a bit confused on
whether I should use the state of being for some things, or something like
[this](http://www.japaneseverbconjugator.com/BeingVerbs.asp).

Which of these would be correct?

**Using what the first link says** I am a student = 学生だ I'm not a student =
学生じゃない I was a student = 学生だった I was not a student = 学生じゃなかった

**OR**

**Using what the second link says** I am a student = 学生です I'm not a student =
学生ではありません I was a student = 学生でした I was not a student = 学生ではありませんでした

Would both be correct to use, depending on the situation? Like, would the
state of being be more for if I wanted to be more declarative when saying
something? As far as I know, it can only be used on nouns, and na-adjectives.
Would both technically be correct or would one be more natural than the other?
Would the first method be the more informal way of speaking, where as the
second method would be more formal, or am I completely missing something? I'm
hoping someone can clear this up, I know it's really basic stuff, but I'd
rather not mess up something simple, and cause myself problems, in the future.

