Commerce: How to implement/save 'Use shipping for billing' field for future orders
We achieve this by simply checking the ids of the addresses set on the cart.  Commerce saves the last used shipping and billing address for customers, so you can just use some simple template logic to achieve what you want I think:

        {% set sameAddress = true %}
        {% if cart.shippingAddress and cart.billingAddress %}
            {% if cart.shippingAddress.id != cart.billingAddress.id %}
                {% set sameAddress = false %}
            {% endif %}
        {% endif %}

        &lt;div class="same-address-checkbox"&gt;
            {{ forms.inputCheckbox({
                type: 'checkbox',
                id: 'sameAddress',
                name: 'sameAddress',
                checked: sameAddress,
                value: '1',
                label: 'Use same address for billing address?',
            }) }}
        &lt;/div&gt;


One caveat here, if you offer a checkout during registration, you'llw ant to use my plugin for this as otherwise these last used addresses are not copied to the newly created Craft user - https://github.com/bossanova808/CommerceRegisterOnCheckout