Sodium bicarbonate (baking soda) is NOT the same as Sodium carbonate (soda ash).
These two products are often confused. Both raise pH and alkalinity, but soda ash is over 1000-times more concentrated than sodium bicarb.
Sodium bicarbonate (NaHCO3-), also known as baking soda, is the most common dry chemical used in swimming pools. It is the product of choice for increasing total alkalinity because it directly adds bicarbonate to the water. Sodium bicarbonate only has a pH of about 8.3, so you can add a lot of it to the water to increase alkalinity while having only a minimal impact on the pH.
Sodium carbonate (NaCO3--), also known as soda ash, is rarely (if ever) used to treat residential swimming pools. It is primarily used in commercial pools with automated pH controllers that feed acid. This is the product of choice to raise pH with a minimal impact on total alkalinity because soda ash is highly concentrated. A little bit of soda ash can raise the pH substantially because soda ash has a pH of about 11.3.
Soda ash's 11.3 pH compared to sodium bicarb's 8.3 pH means that soda ash is about 1000x more basic than bicarb.
Which product is right for my pool?
Sodium bicarbonate is the preferred product, by far.
Unless you have chemical automation and an acid feeder, you should never need soda ash. This is because pH naturally rises due to CO2 loss, so there's no need for a chemical like soda ash to raise your pH. Just let it happen naturally. The only pools that might want to use soda ash are commercial pools with acid feeders that need a way to boost pH with only a minimal impact on alkalinity.
Sodium bicarb, however, is likely to be used in every pool in the world. It is by far the product of choice for increasing alkalinity. It can do this because total alkalinity is the sum of all dissolved alkali in the water, measured in ppm (mg/L). Pound for pound, sodium bicarb and soda ash raise alkalinity by about the same amount. The difference is if you add a lot of soda ash, the pool will cloud up because the pH will be MUCH higher, forcing an LSI violation.
In other words, a very small amount of soda ash raises the pH strongly, whereas it takes a LOT of sodium bicarbonate to raise the pH the same amount. So you can use much more sodium bicarb at a time to raise alkalinity without raising the pH too much.
If you don't know what you're doing with soda ash, don't use it.