The tax liability report will only include data for taxable invoice line items belonging to closed invoices, where matching tax rules still exist and the invoice was closed between the given dates.
The transaction reports will include all transactions received/applied, where the transaction was created between the given dates.
So, if you have paid invoices with line items that are not taxable, or partially-paid invoices, or you have deleted tax rules, or transactions were created before your start date, but applied to invoices after the start date, then the tax liability report total would appear less than transactions'.