I agree with others' answers. The meanings overlap. It is hard to think of an example where you couldn't interchange them. Mostly, it's a difference in tone.
"Objective" sounds important, dignified, formal--and a little evasive.
"Target" sounds forceful, direct, and motivational.
"Our target is..." would often be followed by a number, like "...$50 million in revenue for 4Q2015."
"Our objective is..." would often be followed by something vaguer and broader, like "...to improve customer communications."
A "target" is a noun you can draw a picture. It has concentric circles and a bullseye. There's a certain feeling that you'd like to hit the bullseye, but that if you did, you'd celebrate the accomplishment, and that it is a quick process--you take a shot, you either hit the target or you don't, and then it's over.
An "objective" isn't a physical object you can draw a picture of. When I think of an "objective" I think of a hill with something at the summit, and you are expecting to climb the hill and reach that summit--quickly or slowly, but you need to get there and you expect to get there.
But once again these are just vague differences in tone.
Here are some examples I found with Google--I've selected ones that I think are typical:
"Our target is to create a million jobs by 2020."
"Our target is a national network of 1,000 computer learning centres"
"In 2035, our target is 13 percent reduction – the regional plan will achieve 21 percent."
"Our objective is to improve the quality of their workplace experience."
"Our objective is to encourage and support a new generation of entrepreneurial ecological farmers. "
"Our objective is simple, to ensure the right insurance products are available for Toyota customers, at the right time, at the right price and to the right quality."