Account manager is an employee who is tasked with day-to-day support of a particular customer's account with a business, and who serves as the primary point of contact between the customer and the company. The account manager position can provide customer support, technical support, planning and optimization for the account, as well as developing a relationship with the customer. maybe your refering to customer service manager it deal with customers on a daily basis. This includes all customers, even the rowdy ones who want something for nothing. Good customer service managers know how to keep all customers happy and diffuse potentially volatile situations. cowboy...

In my opinion, 'account manager' who in charge of the client resources and work closely to their key clients in daily working. But for 'customer manager', I'm not sure, maybe it isn't a common or formal title, maybe it means customer service manager.