Transactional email services deliver automated messages triggered by an application: order confirmations, invoices, password resets, login links and notifications. They provide an SMTP relay or an API, manage sender authentication and reputation, and report on delivery, bounces and complaints.
These messages often contain personal data and secrets: names, addresses, invoice details and one-time links that open an account. The provider processes that content, normally logs it for some time, and holds the reputation of your sending domain. If the provider falls under non-EU law, as with Amazon SES or SendGrid, or stores content outside the EU, the rules on international transfers come into play. Moving is technically simple because SMTP is a standard, but deliverability is not portable: IP reputation and domain warm-up must be rebuilt, and templates, suppression lists and webhooks have to be migrated.
When choosing a European option, ask where sending servers and logs are located, how long message bodies are retained and whether content logging can be turned off, and whether DKIM, SPF and DMARC are supported on your own domain.