The padding inside a table-divider (TD) is a padding property applied to the cell itself.
CSS
td, th {padding:0}
The spacing in-between the table-dividers is a space between cell borders of the TABLE. To make it effective, you have to specify if your table cells borders will 'collapse' or be 'separated'.
CSS
table, td, th {border-collapse:separate}
table {border-spacing:6px}
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