It depends what you mean by the same. As far as I can tell the Sodium Hypochlorite constituent of both is the same. However, I'm no expert, so I'll cut and paste what Chem Geek posted.
'6% Bleach is, by weight, 6.0% sodium hypochlorite (i.e. chlorine), 4.7% salt, and 89.3% water. All sources of chlorine will add salt to the pool as chlorine turns into chloride (salt) when it gets used up, but bleach adds salt upon addition as well.'
and...
'For every 10 ppm FC added by ANY source of chlorine, it will result in 8.2 ppm salt from the consumed chlorine that turns into chloride salt. With bleach, chlorinating liquid, and lithium hypochlorite, there is an additional 8.2 ppm salt upon addition so the net total result is 16.5 ppm.'
So I interpret that as you would get additional salt from using bleach instead of sodium hypochlorite. Why additional salt is added to bleach I don't know, and CG didn't say. (Perhaps he will here, and correct my chemistry.)