I will tell you my experience with the Air Force. When I was getting my medical one year ago, the limit was 20/50 correctable to 20/20 in each eye. I have heard now that they are thinking about changing it to 20/200, but it could have just been a misinformed recruiter. Since I am 20/50 I would really like some breathing room so I hope it is true.
As far as different vision standards for each type of flying, that is not true for the Air Force and I imagine it is the same for the Navy. They can't tell if you are going to be a fighter pilot or a cargo pilot when you apply and they don't want to invest a large amount of money training someone who is limited to a specific type of airframe.
And don't get any eye surgery until after you talk with a recruiter. If it doesn't meet their standards, you will be denied no matter how good your eyesight is now.