"The student gets up in the morning."
Translation:학생은 아침에 일어난다.
The first one is the so-called diary form, rarely used in conversation. It lacks any politeness level. It is not directed to anyone in particular, to make a neutral statement about a fact. It's an important tense to know if you want to pass the written portion of the TOPIK exam.
More info here too (see an important note before you begin section).
The second one, I guess you're already familiar with it by now.
In my experience, both of them are used about the same rate colloquially. I've heard my parents and their friends use both forms depending on the context.
If the person is authoritative or old-fashioned, that's possible. Usually, one uses 해체 instead of 해라체.
I think the page is talking about 하라체, which this course does not cover. 하라체 happens to share all endings with 해라체 except imperative endings. So you are right in a way, but we intended to teach 해라체, which is the lowest politeness level.
일어나 = informal low 일어나요 = informal high 일어난다 = formal low 일어납니다 = formal high