soda ash is sodium carbonate. pH up is typically sodium bicarbonate.
Sodium carbonate (soda ash) has a pH of 13.0 and contributes carbonate to total alkalinity. Because it has a high pH, soda ash will raise both pH and total alkalinity. 1 lb of soda ash added to 10,000 gallons of water will increase TA by 11.33 ppm and will increase the pH by about 1.0 unit.
Sodium bicarbonate (sodium bicarb, bicarb or baking soda) has a pH of 8.3 and contributes bicarbonate to total alkalinity. Because the spa water pH is close to the pH of the bicarb, it will have a greater effect on TA than pH. So if you want to raise just the alkalinity with a small rise in pH, use bicarb. 1 lb of bicarb added to 10,000 gallons of water will increase TA by 7.15 ppm and increase pH by about .1 to .2 unit.