Overwrite:
vendor/magento/module-checkout/view/frontend/web/template/billing-address.html
in your custom theme:
app/design/frontend/<customTheme>/<customTheme>/Magento_Checkout/web/template/billing-address.html
And remove:
<div class="billing-address-same-as-shipping-block field choice" data-bind="visible: canUseShippingAddress()">
<input type="checkbox" name="billing-address-same-as-shipping"
data-bind="checked: isAddressSameAsShipping, click: useShippingAddress, attr: {id: 'billing-address-same-as-shipping-' + getCode($parent)}"/>
<label data-bind="attr: {for: 'billing-address-same-as-shipping-' + getCode($parent)}"><span
data-bind="i18n: 'My billing and shipping address are the same'"></span></label>
</div>
So the overwritten file should be like this:
<div class="checkout-billing-address">
<!-- ko template: 'Magento_Checkout/billing-address/details' --><!-- /ko -->
<fieldset class="fieldset" data-bind="visible: !isAddressDetailsVisible()">
<!-- ko template: 'Magento_Checkout/billing-address/list' --><!-- /ko -->
<!-- ko template: 'Magento_Checkout/billing-address/form' --><!-- /ko -->
<div class="actions-toolbar">
<div class="primary">
<button class="action action-update" type="button" data-bind="click: updateAddress">
<span data-bind="i18n: 'Update'"></span>
</button>
<button class="action action-cancel" type="button" data-bind="click: cancelAddressEdit">
<span data-bind="i18n: 'Cancel'"></span>
</button>
</div>
</div>
</fieldset>
UPDATE:
In later versions of Magento, keeping line
<render args="detailsTemplate"/>
prior to
<fieldset class="fieldset" data-bind="visible: !isAddressDetailsVisible()">
is important to retain the functionality.