The corrected answer: It seems that the both rows from your table show the same thing: the sum amount of all vitamin A-related substances, but in different units; the 1st row in RAE and the 2nd row in IU.
As I said before, according to ods.nih.gov, 1 IU retinol = 0.3 mcg RAE, but this conversation is true only for retinol (the true, "pre-formed" vitamin A), which is found only in animal foods.
The main vitamin A-like substance in plant foods, such as carrots, is beta-carotene and the conversion rate is: 1 IU beta-carotene = 0.05 mcg RAE, so the 20-fold difference between 835 mcg RAE and 16,706 IU now makes sense.
Why to complicate this?
Large amounts of vitamin A (retinol) can be toxic. The upper tolerable level (the amount that should cause no side effects and is not nearly toxic) for retinol for adults is 3,000 mcg RAE. For example, 100 g of chicken liver contains 4,296 RAE of retinol. (You can also see that for the liver, 4296 RAE/14378 IU = 0.3, so this explains again that the two rows are the same thing.)
You can see that the same IU of vitamin A in animal foods is translated into much more RAE than in plant foods. This is also why high IU of vitamin A in animal foods can be (potentially) much more toxic that the same IU of plant foods.