How to determine where the CCK fields are stored in database? When a content type is created, there is a new table for it. For example, there is a content_type_claim table, for content type claim. Content fields are defined within the table.

However, when a content field is shared (used more than once) in different content types, there will be another table created for this field. For example, there is a content_field_claim_no table for claim no, if claim no is also used in another content type.

My question is, in which table Drupal defines whether a content type field is stored inside the content_type_??? table (when used once), or in its own conten_field_??? table (when used more than once), for a particular content type.
You want the content_node_field_instance table. As that table defines each "instance" of a field on different content types. For the field configurations (global configs, independent of instance configs) you want the content_node_field table.

Similarly in Drupal 7 there's field_config table for global field configurations, and field_config_instance table for each instance of a field with content types.