Manipulation of controls in Excel confused me for a while until I realized that there are two kinds of them, and this might be part of your confusion. For example, there is:
a Form Control Combo Box, and,
an ActiveX Control Combo Box.
The two look, behave, and are controlled similarly, but not identically.
Click image to enlarge:
I realize that wasn't your question, but I figured I should make sure you can identify which control you are using, and therefore make sure that you're using (and Googling) the correct information - especially since the terms "Combo Box" and "Drop Down Box" are often used interchangeably. A Google Search for Vcode related to BA Combo Box Control will be wrong 50% of the time, so you need to be more specific.
AS for the code difference:
FORM CONTROL Combo Box
'add item
ActiveWorkbook.Sheets("Sheet1").Shapes("Drop Down 1").ControlFormat.AddItem "abcd"
'remove all items
ActiveWorkbook.Sheets("Sheet1").Shapes("Drop Down 1").ControlFormat.RemoveAllItems
'https://analysistabs.com/vba-code/activex-controls/combobox/
ACTIVEX CONTROL Combo Box
'add item
ActiveWorkbook.Sheets("Sheet1").ComboBox1.AddItem "abcd"
'remove all items
ActiveWorkbook.Sheets("Sheet1").ComboBox1.Clear
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