A transaction identifier is a general term for what is often called a transaction reference number: a unique code attached to a single payment so that banks, processors, merchants and customers can find it, match it and investigate it. The main entry covers how reference numbers are generated and used in everyday payments.
The more generic phrase is common in technical specifications, where a payment may carry several identifiers at once, each assigned by a different party. In ISO 20022 messages, for example, a credit transfer can carry an end-to-end identification set by the payer, an instruction identification and a transaction identification set by banks, and the UETR that follows a cross-border payment through every bank in the chain. Card payments use their own set, such as the retrieval reference number and the acquirer reference number, which is used in disputes.
On blockchains, the equivalent is the transaction hash, which is derived from the transaction data itself rather than assigned by an institution. Whichever system is involved, a good identifier is unique, travels unchanged with the payment and is stored by every party.