UPDATE is an example of DML (Data Manipulation Language) statement. As such it is used for modifying/updating the data within a table column or group of columns.
ALTER/MODIFY is an example of DDL (Data Definition Language). This statement is used for changing (modifying) the metadata (structure) of an object like for example adding/removing column, index, etc.
MODIFY clause is used in RDBMS systems like Oracle for changing column definition whereas in some other systems like SQLServer ALTER COLUMN is used instead