"I really want to drink."

Translation: Я дуже хочу пити.

[SweetDog_37]

So for this sentence it gives two translations but I am a bit stuck on two words.
One sentence reads: Я дуже сильно хочу пити
and the Other as: Я дуже бажаю пити
What do сильно and бажаю mean?

[3june1957]

The above anglicized option was not given in the choices.