StringBuffer allows modification of a string by providing methods to append, insert, replace, and delete portions of the string. It maintains an internal cursor that tracks the current position during these modifications. StringTokenizer breaks a string into tokens based on delimiters and also uses a cursor to iterate over the extracted tokens. Common methods for both classes include nextToken() to return the next token, countTokens() to get the number of remaining tokens, and hasMoreTokens() to check if additional tokens exist.