`RETURN NEXT` vs `RETURN RECORD` in PostgreSQL

While RETURN NEXT is valid plpgsql syntax, RETURN RECORD is non-existent as such. It corresponds to how you declare the return type in the function header. Read the manual about how to return from a function.

In a function declaring RETURNS int you can:

RETURN 1;

For RETURNS SETOF int you can:

RETURN NEXT 1;

If you declare OUT parameters, you can just:

RETURN;
-- or do nothing: OUT params are returned at the end of the function anyway

Or if you combine OUT parameters with RETURNS SETOF record - effectively the same as RETURNS TABLE (...):

RETURN NEXT;

The current state of all OUT parameters is returned as next row.

Finally, to return a whole set of rows at once:

RETURN QUERY ...

record is a special data type. It's meaning depends on where you use it. Like I posted in my answer to your previous question:

• Declare variable of table type in PL/pgSQL

The manual about the record type in PL/pgSQL.

A RETURN NEXT statement:

• can append zero or more rows to the function's result set one by one and the rows can be modified one by one.

• cannot exit a function while a RETURN statement can.

• can work only in a PL/pgSQL function.

• can work only with SETOF <sometype> or TABLE() in a RETURNS clause otherwise there are the error and the error.

*The doc explains RETURN NEXT statement in detail.

A RETURN QUERY statement:

• can append zero or more rows to the function's result set at once and the rows cannot be modified.

• cannot exit a function while a RETURN statement can.

• can be used with SELECT or VALUES statement.

• can be used with INSERT, UPDATE or DELETE statement with RETURNING clause.

• can be used with EXECUTE statement to be dynamic.

• can work only in a PL/pgSQL function.

• can work only with SETOF <sometype> or TABLE() in a RETURNS clause otherwise there are the error and the error.

*The doc explains RETURN QUERY statement in detail.