These are two different things:

 Asset Management connotes something more passive: a custodial and care-taking function over assets under administration – for example, the management of physical plant and equipment is asset management. To apply this term to fund management or discretionary management of financial portfolios is inappropriate while Investment management connotes something more active: that is, discretion as to the investment decision. This means the action of deciding whether to buy, sell or hold the asset. – Source: wallstreetoasis.com