This is an excellent question, but the answer may take a while and be a bit technical so please bear with me:
Firstly, let's start with anatomy. The septum is the major structure that gives our nose its shape and size. It's primary function is as the skeleton for the nose. This enables the nose to stay wide open and not collapse when we breathe.
Biomechanically, the most crucial portions of this support is in the L strut - An L shaped portion of the septum that forms the top and front portion of the septum. As long as you maintain a strong L strut, you can essentially remove the central part of the septum with no issues.
Septoplasty is referring specifically to either removing or weakening only the central portion of the septum. The L strut is left untouched.
This works well when the problem is only in the central septum. But what if, the problem is in the L-strut? You will then need to repair the L strut. This is called septorhinoplasty, or rhinoplasty for short.
To complicate things a bit more, there are also other structures in the nose that affects the airflow, such as the internal and external nasal valve. Again, these are not addressed in a Septoplasty, but would be addressed in a rhinoplasty.
To summarise, from a breathing perspective, there can be one or many problems involving the central septum, L strut, internal nasal valve, external nasal valve, turbinates.
Septoplasty addresses only central septum deviations. Septo rhinoplasty addresses everything including the central septum.
From a cosmesis perspective, since Septoplasty only addresses the central septum, you do not expect any changes in the appearance of the nose. A rhinoplasty can and will change the appearance of the nose.
Since you mentioned you have a crooked nose, there is a good chance this is due to deviations in the L strut (central septum is not visible externally).
This might mean that doing a Septoplasty alone may not be enough to solve your breathing issues, and will certainly not straighten the nose. A rhinoplasty will be able to address both.
