Hard delete means that the records are permanently and instantaneously deleted, once hard delete happens you can not reference or count the records.
This means any third party applications that you use to pull your Salesforce data, like Terminus, will still contain these hard deleted records until we do a full data refresh.
A regular delete will put records into the recycle bin, these will stay there for a "period" of time, which is usually 15 days but may be less depending on other variables; reference this doc for additional details. Third party applications like Terminus will count and delete these properly.
It is recommended to never use hard delete and only use the normal delete functions.