While these two are similar, there are several key differences, especially when it comes to grant proposals.
Goals are more general, while objectives are specific.
When applying for a grant, the key is to make sure that your goals are the same as the funding source's goals. If you do not know what the funding source's goals are, then you better find out. If there is no way to measure whether or not your objectives have been met, then there is no way to determine whether or not the grant money was wasted. At the end of 1 year it will be very simple to determine whether or not the objective was met. Your project must fill specific, quantitative needs.