what is the difference between asset and property management? 

Here is the basic difference, and then we'll let the professionals expand on my definition. 

Property management is the day-to-day management of the property, including leasing, collecting rents, paying the bills, and maintenance, etc.  Property management ensures that the day-to-day property management functions are efficient and that the property is fully leased and is producing a good rate of return given its current use.

Asset Management ensures that the property is constantly evaluated for its best possible use and makes changes when appropriate to increase the value of the property, including recommendations on when to buy, hold and sell.