Cost object is an item of expenditure like salary,rent etc.
Cost center is an area of activity. it could be activity of
income  or activity of expenditure. When an activity center
is comprises of only expenditure it referred as cost center.
when the activity center has both income & expenditure
related to it, it is referred as Profit center. For e.g. a
regional sales office is a profit center. it can generate
income (sales), it also relates expenditure like salary,
rent, advertisement,stationery etc. HR dept in an
organization is a cost center since it is only a service
dept for internal requirement of the organization.

cost center is a type of cost object. Cost object is one 
where costs are captured

Cost object may be a product,location of the organisation 
or a service center.cost center means any dept or machinary 
or anything of the organisation which is responsible only 
for cost.it is also a classification under cost object.