Depending on the culture she is from, there may be things that she wants to do, that she cannot, without getting married. Examples are:
- Having sex with her boyfriend
- Living in the same house as her boyfriend
- Having a baby which would not be referred to as "illegitimate"
- Purchasing major things (such as a car)
- Travelling without a chaperone, such as her brother
Perhaps when she was younger she innocently thought all these things were possible to her without having to marry. Now she is older she realizes that she "has" to marry to achieve them.
Does it mean she is getting used to the idea of getting married?
Not necessarily. The phrase used suggests that she is getting used to having to marry to do certain things.
Is there a difference between the two sentences?
Yes there is. One is considering the requirement to marry in order to do things. The other is considering an imminent marriage.
The lady in question might never marry, conceivably. She might tell her friends "I never realized I had to marry to do X. I didn't want to marry, so therefore I can't do X.".
Of course, this is all dependent on where you live. In some cultures you can do many things without being married.