Is it possible to make only the shipment number equal to the order number and leave invoice number unchanged?

Yes, such a setting is easily achievable due to flexible extension settings. Each option – Invoice, Shipment, Credit memo numbers – can be set to either be the same as order number or different.

In case if you need to have the shipment number the same as the order number but configure the invoice number independently, you should choose the following settings in System > Configuration > Custom Order Number:

Magento Custom Order Number extension by Amasty

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