Chromatid is the single arm of chromosome. Two chromatids joined to centromere make a chromosome. During replication of DNA, chromatids undergo duplication forming identical copies of chromatids. Identical copies (original and duplicated) of chromatids are called as sister chromatids. These sister chromatids are then separated during mitosis and go to each daughter cells during after the cell division.
Homologous chromosomes are the pair of chromosome containing same genes but might with two different alleles. Each one of the chromosomes is inherited from one of the parent. They are not identical as they come from different individual. They pair up during first meotic division and get separated and go to daughter cells.