A TLS server must send its leaf certificate first, followed by the intermediates (RFC 9846 §4.5.1 lets the remaining certificates come in any order, but older clients expect issuer order). The root is normally omitted because the client already has it. A missing intermediate is the classic "works in my browser, fails in curl" error: browsers may fetch it through the AIA caIssuers URL or reuse cached intermediates, while OpenSSL, Go, Java and most API clients do not.
Clients build a path, not just read the list: with cross-signed intermediates several valid paths can exist and the verifier picks one that ends at a root it trusts. That is how Let's Encrypt kept old Android devices working through the DST Root CA X3 cross-sign until 2024, and it is why the order in the file matters less than whether every needed certificate is present.
PEM bundles (fullchain.pem) hold the leaf and intermediates; PKCS #12 files can carry them too. The chain builder reorders and completes a chain, and the PEM bundle splitter separates a bundle into its certificates.