I'm trying to figure out if I can have 2 different domains that I would like to use for my store. for example: www.example.co.uk and www.example.eu
One will be used for Sterling and the other for Euro payments. Can this be done?
yes, this is possible. you need to create 2 websites in Magento 2 admin and add Base url for specific website.
Also you need to create symlinks in second domain for these folders
Yes, it is possible to create 1 website with 2 domains. But make sure you purchase a subdomain to avoid content duplication so that your website can rank on the search engines.
Magento is best for eCommerce and that's why it offers you to easily utilize the Magento feature to use 1 store with domains.
Hope this information will help you!
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You only need to do simple settings, you can achieve your needs.
Follow this tutorial to achieve.
How to setup Multiple Domains in a Multi-Store Setup - Magento 2 Tutorial