Generally speaking, objectives are more narrow than goals, which tend to be less specific. In practical terms, a learning objective might be covered in one or two classes, while a goal might encompass one or two units.
Using the North Carolina United States History Standard Course of Study as an example, Competency Goal 1 is to "identify, investigate, and assess the effectiveness of the institutions of the emerging republic." Clearly this is a very broad subject. It is thus broken into three more specific objectives, the first of which is to "identify the major domestic issues and conflicts experienced by the nation during the Federalist Period."
Another way of thinking of it is to look at objectives as being "unpacked" from goals. If a student is to meet a learning goal, they would need to master each objective. Often goals are themselves drawn from broader learning "strands" or "themes." So in a word, goals are broad, objectives more narrow.