Wealth management has a lot of similarities to investment management also a lot in common with finance management. But the finance management defines more corporate not a personal finance management, while the wealth management is only for individuals.
Wealth management is a wider spectrum of services than only investment management. Next to the investment consultancies or trading on the client's account it also includes personal finance and private banking attributes: can provide all banking products like cards, loans and other, accounting and legal services, tax consulting.
Wealth management is provided by investment banks or investment branches of regular banks, brokerage firms. Usually this service is not cheap and suited only for the richest people who can afford it also are so rich that doesn’t have time to take care on their wealth by themselves. If you think you are one of them but do not know how to choose a proper wealth manager then you can try use similar criteria as was described for choosing an investment manager.