Applying a digital signature adds metadata on a document without modifying its content (thus without impacting its integrity). This is how multiple signatures can be applied to a document while preserving the document’s integrity.
A visible signature includes a metadata that holds a visible marker (signature appearance) when viewing the document, showing that it has been signed.
An invisible signature omits this visible marker.
Both types of signature ensure the integrity of the document. The digital certificate information can be seen with both types when validating a signature. A visible signature, however, can appear on physically printed documents (this can be useful if printed copies of documents are also used or archived).
You can choose to use visible or invisible signatures according to your company policy.