They would be the same ranks as a Navy ship.
The actual positions, however, depended on the era in question.
In the 24th Century (in which all series except for the original series and Enterprise take place), the specialized positions include Captain, Commander, Operations Manager, Helm, Tactical, Security, Engineering, Medical, Science, and Counselor.
The 22nd-23rd Century was roughly the same, with the exception that specialized but similar positions such as Tactical/Security and Medical/Science were often combined. Also, the position of Counselor is exclusive to the 24th Century.