Volitional form + omoimasu

I've recently learned about volitional form and to omoimasu from Genki 2 textbook.
Genki explains this form as meaning to decide something, but most other places I've looked say that it's not used as such a strong thought. Merely, I've been thinking.
Genki says
毎日三時間日本語を勉強しようと思っています
Translated as: I've decided to study Japanese for three hours every day
But other sites have said
母に手紙を書こうと思っています
Translated as: I am thinking I will write a letter to my mother

And if it is just 'thinking' of doing something, when do I know to use volitional + と思う or just plainと思う?
Thanks

Trying to come up with exact equivalent in English might be a bit tricky, but I might translate that as “I intend to…” In my view (I’m native speaker of Japanese by the way), because it doesn’t involve an action of “deciding” something, but a certain degree of determination/intention is there.

So if i list up sentences in Japanese, ranging from high certainty that you will do something, to less certain, it might be something like (excuse me if there are any expression/construction you have not yet learned):

母に手紙を書きます。
母に手紙を書くつもりです。
母に手紙を書こうと思っています。
母に手紙を書こうかと考えています。
母に手紙を書くかもしれません。

Different people perceive phrases slightly differently, so I hope others might contribute too.