Managers play a vital role in the career of artists, songwriters, producers, and musicians. It's is important to know the different types of managers in the music industry and their role(s), in order to determine what you "the talent" really needs in order to move forward with you career. Most artist have more than one manager, it often depends on the stage of ones career.
Music Managers (aka Artist Manager, Talent Manager, Personal Manager)
A Music Manager's role is to plan, organize, develop and guide the overall career of the client. This is perhaps the most important person (or team) in an artist's musical journey. Although not part of the job description, Music Managers often serve as personal counselors for their client as well, in order to ensure that their personal life does not negatively effect their professional one.
Business Manager
A Business Manager's role is to manage the income and expenses of the client. Business Managers usually take care of making payments on behalf of artists, as well as providing overall financial advise with regards to investments and asset management. It is important that your Business Manager has an accounting background as this will become very important once you are profiting from your talent. Especially, when most artists don't consider tax obligations related to their income (particularly performance income) and/or payments made in the form of CASH.
Road Manager
A Road Manager takes care of the artists while "on the road" (or on tour). Their overall goal is to ensure that the artist is able to focus solely on their performance. The Road Manager ensures that the promoter or booking agent and met all of the obligations of the performance agreement (i.e. payments, accomodations, proper equipment, security, etc.).
Tour Manager
A Tour Manager supervises and coordinates all of the road managers. For new artists or independent labels sometimes the road manager and tour manager are the same person. The difference between the two is that Road Managers tend to focus on one "show at a time" and a Tour Manager usually oversees a string of performance and is in charge of additional details such as merchandising, and tour routing.
Production Manager
A Production Manager handles the the "production of the show". They ensure that the sound, lighting, staging, etc meets with the the artists requirements. Obviously this requires them to work hand-in-hand with the Tour Manager (or Road Manager). Usually only Major Recording Labels employee production managers.