I agree with the previous response, but would like to add a few thoughts of my own. In The Giver, everyone is the same in that all lack feelings because these are chemically suppressed. But all are not equal at all. There are people who are in power who have made the decision, for example, that people's feelings must be chemically suppressed, that weather must be rendered non-existent, that history be wiped out, and that certain people will be given certain occupations. Equality does not exist in spite of sameness because of this. The Giver, Jonah, and Gabriel, of course, are not the same as the others, and that is what allows us to see how dreadful sameness really is.
Being equal to someone does not mean being the same as them. In "The Giver," there are examples of both of these.
Equality just means being treated the same as everyone else -- having to follow all the same rules. So, for example, everyone in the community has to follow the same rules, but Asher and Jonas are not the same at all. Asher is way more goofy and Jonas more serious, but they are both equal because they must follow the rules.
In a very fundamental way, though, everyone is the same in the community. They all have the same lack of feelings and emotions.
In The Giver Equality provides that everyone is allowed the same benefits of the society that others are. Sameness provides different age groups certain equal "privileges"; however, it mainly limits members of the society to conformity in thought, emotion, and action.
One of the first memories that the Giver provides Jonas is that of snow and sunshine. For in the world in which Jonas lives, even the weather is unvarying.
The grey, climatic "sameness" is an objective correlative of the community's strict regulation of difference and variety in all walks of life. (Enotes)
This sameness stultifies any individuality. Creativity is stunted, initiative denied, emotions suppressed, hormonal activity eradicated. In short, individual actions are discouraged and adherence to the rules of a controlling society are given precedence. Consequently, creativity is non-existent, and the superiority of one individual over others does not occur. Thus, incentive to achieve and break from the norm are eliminated and the supposed safety of conformity is achieved.
No one mentioned such things; it was not a rule, but was considered rude to call attention to things that were unsettling or different about individuals. (Ch. 3)
While Equality provides everyone the benefits of the society without exception, there are no opportunities other than those dictated by the leaders. Therefore, this equality is very limited. In fact, it is this stultifying sameness and equality against which the intelligent and independent-thinking Jonas rebels after he becomes the Receiver and is exposed to what has been sacrificed in order to attain Sameness and Equality. For he realizes the many restrictions placed upon individuals in his society.