If you supply goods to a customer in another EU country who isn't registered for VAT in that country, and you are responsible for delivery - that is, they don't collect them - then this is called a 'distance sale'. The most common examples are mail order or Internet sales to private individuals in another EU country.
However, if you transfer your own goods to another EU country - whether to another part of your organisation, or simply to put in storage - this is treated as if you had made an acquisition in the destination country. You therefore have to account for VAT in that country, and if you're not registered for VAT there, that means paying VAT.
If you sell goods or services to someone who isn't VAT registered in another EU country, you must charge VAT in the normal way - just as you would for a UK customer.