There are three options when you click ADD CREDIT NOTE on a Customer Invoice or Vendor Bill:

Create a draft credit note - You will be able to edit and validate this credit note directly or keep it draft, waiting for the document to be issued by your supplier/customer.

Choose this option for traditional credits that you want to issue for Customers after you have sent them the Invoice (such as a reduced price for an incorrect order, damaged item, delayed delivery, etc), or if you receive a credit from your Vendor.

Cancel: create credit note and reconcile - Use this option if you want to cancel an invoice you should not have issued. The credit note will be created, validated and reconciled with the invoice. You will not be able to modify the credit note.

Choose this option if you made a mistake with the Invoice or Bill and you want to reverse it to take it off the books.  You then either don't create a brand new Invoice / Bill or you do - starting again from scratch.

Modify: create credit note, reconcile and create a new draft invoice - Use this option if you want to cancel an invoice and create a new one. The credit note will be created, validated and reconciled with the current invoice. A new draft invoice will be created so that you can edit it.

Choose this option for the same reasons you choose the second option EXCEPT that the mistake was minor and you don't need to start from scratch - you can benefit from a draft copy of the original that you can fix the mistake on.

You don't see the Invoice (or Bill) as cancelled with these options because they are not cancelling the Invoice or Bill by putting it into a cancelled status, they are "cancelling" the Invoice or Bill by creating a Credit Note that reverses and removes the effect of the original Invoice or Bill.

In some jurisdictions you cannot (legally) cancel an Invoice once it has received a number. 

Even if you are legally allowed to cancel an Invoice, you should NEVER do this if your Customer has received the Invoice (because they will enter it into their Accounting System AND it is a binding legal document once you have sent it).

If you are allowed to cancel Invoices, want to move them into a cancelled status (and have not sent the Invoice to your Customer), install the module Cancel Journal Entries and configure the Customer Invoices Journal (and others if needed) to allow you to Allow Cancelling Entries (this option is shown in Developer Model on the Journal Form View).