VAT compliance rules are usually governed differently depending on whether the taxable supply is a service, or the provision of goods. Therefore, the legislation is quite clear if there is an easy distinction.
However, when goods are provided as a supply, they may also require assembly or installation. (i.e. the supply is goods and an associated service). If this is being done in a foreign EU member state, then there may be an obligation to register as a non-resident tax payer.
The supply and installation of goods is treated as a supply within the country where the assembly takes place. This generally triggers an obligation to register for VAT under the EU VAT Directive.
However, most EU member states now offer exemptions under the VAT reverse charge rules, or provide some sort of thresholds, so VAT registration by a foreign supplier is rarely required.