On-line arithmetic vs digit recurrence, are they different?
There seems to be substantial difference between on-line arithmetic (as described in your link) and digit recurrence methods (as described here for example). The only resemblance between the two methods is that they are both sequential.


on-line arithmetic processes long numbers one digit at a time, without waiting for the whole numbers to be there. For example, if you compute XXX2+YYY3, you know the result will be ZZZ5 without receiving any more digits of X and Y. In the next step, when one extra digit of each operand is available (e.g. XX72+YY53) you will be able to produce one extra result digit, ZZ25.
digit recurrence methods use recurrent formulae to implement certain operations like division. They operate on all digits of the operands on every step, but the result becomes more and more precise as the number of steps increases. For example, if I need to compute 123/7, I could conclude after step 1 that the result is 10 and the remainder is 53. In the second step I will further divide my remainder and update my result to be 17 with the remainder 4. If it's the integer division I'm after, that would be my final step.