Yes, there is usually a small ion exchanger in the dishwasher to soften the water. The small 1 kg packs are simply more practical for the dishwasher, but they are both 100% sodium chloride with a little anti-caking agent. Table salts are rather unsuitable for dishwashers because of the additives (iodine, fluorine, possibly others).
This is how the Swiss salt works describe it:
What quantity and form should you buy?
Smaller appliances such as dishwashers are filled with 1 kg of regenerating salt. This will last for a while. You can find the 1 kg pack in your local retailer.
Larger bags are worthwhile if you have a house with a water softening system, for example. You can order your regeneration salt online from us or buy it from a wholesaler or retailer near you.
We sell loose salt and evaporated salt tablets. The latter do not contain any (water-soluble) anti-caking agent. If you operate a swimming pool and disinfect it using electrolysis, you should use tablets.