Don't ask me how I know this, but there's two branches under Critical Hit Rating. Critical Power and I think the other is called Critical Strike. That's their official internal Development names.

Critical Hit Rating is just our flat stat that we see on our Character panel and it's this stat that affects both.

Critical Power is... Critical Power. Our Crit Damage. Critical Strike then is Critical Hit Chance.

Now the issue is that the English Localisation Team are scrubs and forgot to change the tooltips for the new Changes, which is what is causing the issue - or it's probably because they don't want players to know what's going on behind the scenes... (bloody Asian MMOs).

In the JP version however, the tooltip of internal release was changed from Critical Hit Rating to just "Critical", which I assume should of been localised as Critical Strike. Battle Litany is the same.

So no, those two skills do not affect Critical Hit Damage.