I've read the definitions a few times over and I still don't understand the difference.
getActiveCell: Range
- https://developers.google.com/apps-script/reference/spreadsheet/spreadsheet#getActiveCell()
- Summary: Returns the active cell in this sheet.
- Description: Returns the active cell in this sheet.
getCurrentCell: Range
- https://developers.google.com/apps-script/reference/spreadsheet/spreadsheet#getCurrentCell()
- Summary: Returns the current cell in the active sheet or null if there is no current cell.
- Description: Returns the current cell in the active sheet or null if there is no current cell. The current cell is the cell that has focus in the Google Sheets UI, and is highlighted by a dark border. There is never more than one current cell. When a user selects one or more cell ranges, one of the cells in the selection is the current cell.
There's this note in getActiveCell's documentation: (copy-pasted including grammatical errors)
It's preferrable to use getCurrentCell(), which the returns the current highlighted cell.
Which doesn't make it any clearer

