The Onmitsukidō and the second division are not the same thing. Totally different branches of soul society.
And once again, 2nd division is a terrible match for Ichigo. They do evil shit, Ichigo is not into evil shit, disagreement there is the sort of thing that would get him executed.
First of all are highly interconnected, They got 5 subdivision, Ichigo can join any subdivision he wants and he can cultivate his skills and then transfer to another division. look at kisuke's example.
Executive Militia - The first branch of the Onmitsukidō. It is ranked the highest of the five branches in the division. The Executive Militia carries out missions that involve combat. They specialize in the unarmed combat technique known as Hakuda and is able to operate silently and in secrecy. Their main duty is to carry out missions requiring the use of force.Their responsibilities include punishment and assassination of ex-comrades who break the law and acting as scouts during battle against Hollows.
Patrol Corps - The second branch of the Onmitsukidō. Intelligence gathering within the Seireitei. Their appearances are unknown in order to preserve confidentiality. Specifically, they are assigned mainly to the Seireitei area and gathers data on uprisings. In the event of those under house arrest escaping they also are tasked with finding and apprehending them.
Detention Unit - The third branch of the Onmitsukidō. The Detention Unit is responsible for the imprisonment and supervision of all criminals within the Seireitei. They also have another duty known as Special Detention, which concerns those who joined the Gotei 13 but were judged to be a danger to their fellow Shinigami. They investigate, apprehend, and keep these individuals sealed away from the rest of Soul Society within the Special Underground Detention Facility, aka. the Nest of Maggots. It should be noted that those few who are kept in the Maggots' Nest have not actually committed any crime but have been identified by the laws of Soul Society as "Dangerous Elements". This unit acts somewhat similar to a prison and mental rehabilitation center.
Unknown
Inner Court Troop The fifth branch of the Onmitsukidō. The Inner Court Troop serves as the information transmission unit within the Seireitei. A special ops unit that is mobilized whenever a mission is urgent and requires secrecy. Many of its members are masters of Shunpo.