The confusion here is understandable because the two things overlap. An IBAN is not an alternative to an account number, it is a wrapper around one: it takes the domestic identifiers a country already uses and packages them with a country code and a checksum so that a foreign bank can handle them safely. Seeing where one sits inside the other makes the whole international payment form legible.
What an IBAN is made of
An IBAN starts with a two letter country code, then two check digits, then the country's own domestic identifiers in whatever shape that country uses. A United Kingdom IBAN runs to twenty two characters and contains a four letter bank code, the six digit sort code and the eight digit account number. So a UK IBAN literally has the account number inside it, in plain sight, near the end. Other countries package different fields, which is why IBAN lengths differ from one country to the next.
The check digits are the point
The two digits after the country code are computed over the whole of the rest of the IBAN. That makes an IBAN self checking: a receiving system anywhere in the world can tell whether the string it was given is internally consistent before it does anything else, without knowing a thing about the destination country's own numbering rules. That is the problem the IBAN was invented to solve, and it is why international payments quote one rather than a bare account number.
The United States does not use IBANs
This is the single most common source of confusion for American payers and payees. There is no US IBAN. A payment into a US account uses the nine digit routing number and the account number, and for an incoming international wire, the bank's SWIFT code. If a foreign payer's form demands an IBAN for a US account, the correct answer is that the United States does not issue them, and the payer should use the routing number, account number and SWIFT code instead.
When you need both
Within Europe, the IBAN alone is usually enough and the BIC is often optional. Sending from outside Europe you will normally be asked for the IBAN and the BIC together. Domestically inside the UK you use the sort code and account number and never the IBAN. The practical rule is that the IBAN is for money crossing a border into a country that issues them, and the domestic pair is for everything else.
Questions people ask about iban vs account number
Is an IBAN the same as an account number?
No. An IBAN contains the account number along with a country code, check digits and the domestic bank code.
Do US banks have IBANs?
No. The United States does not issue IBANs. Use the routing number, account number and the bank's SWIFT code instead.
How long is a UK IBAN?
Twenty two characters: the country code, two check digits, a four letter bank code, the six digit sort code and the eight digit account number.
Can I work out my IBAN myself?
It can be derived from your sort code, account number and bank code, but use the one your bank publishes. Banks state the IBAN in the app and on a help page for exactly this reason.