In current usage, "sentence" refers to a punishment determined by a court or other legal process. "Condemn" refers to a moral judgment.
"Sentence" always implies a specific punishment, as in, "Mr Brown was sentenced to ten years in prison." You could say someone was sentenced without specifying just what the punishment was, but the understanding would be that there was some specific punishment.
"Condemn" may or may not have any specific punishment. You can say, for example, "The National Prohibition Society strongly condemns all consumption of alcohol." As worded, that statement does not say that they call for making it illegal, just that they say it is a bad thing. (They may indeed want it to be illegal, but that's not what the statement says.) "Condemn" can also be used to describe a punishment that someone suffers, such as "He we condemned to death." It need not be a legal punishment. "Sally's ruthless ambition condemned her to a life of loneliness." You couldn't use "sentence" in that context.