I believe that the "sameness" came around because of a desire to make sure that A) people would not be sad and B) that people would not make bad choices.
If people are not all the same, then some people are going to be better than others. They will be more successful or have smarter kids or make more money. This will cause dissatisfaction among many people who will be jealous of those who have done better. With the sameness, this will not happen.
With the sameness, people will also not make mistakes. They will not choose jobs that make them unhappy. They will not have too many children or get divorced. This will make the whole society run more smoothly.
There are no real differences between people because the community does not want these things to happen.
To book at "The Giver" as it was written, it is somewhat of a socialistic society where everything is meant to be equal. The concept of sameness represents that what is there for one is there for another in the society. In order to carry that out, the people must dress the same, look the same, and live the same.
One thing that is not stressed is that the jobs are not the same. The society like other societies has different levels of jobs. One becomes aware of this when Jonas' sister talks about wanting to be a birth mother. She is quickly told that she does not want to be in the position. In addition, the reader is also told that night nurturers are not as important as day nurturers and so Jonas' father wants to get back onto a day shift.