In some contexts Inshallah and "Bae Ezarat Hashem" could I guess have similar meanings. E.g. in the Wikipedia example: "I will visit my relatives in Riyadh this summer, God willing." it can be used exactly the same way.
Some languages have a distinct grammatical mood[0] for expressing wishes, curses, etc.: things that the speaker would like to pass but may or may not. (here are the dynamics, I think I've set the right initial conditions, but let's integrate them forward...)
Other languages have a distinct grammatical mood[1] for expressing things that, as day follows night, are certain to happen: (here's the Lagrangian, and there's the attractor)
In these senses, בס״ד could be viewed as a syntactic marker for the optative, somewhat like, but much shorter than, "forward-looking statements are provided to allow potential investors the opportunity to understand management’s beliefs and opinions in respect of the future so that they may use such beliefs and opinions as one factor in evaluating an investment."
[I am bitterly disappointed that זב"שך is outmoded]
[0] https://en.wikipedia.org/wiki/Optative_mood
[1] in HWC (alas, it has no wikipedia!), "bumbai" can be used for prophecy: "You stay X, bumbai Y" is IIUC: "if you continue to do X, Y shall come to pass."
Lagniappe: https://en.wikipedia.org/wiki/Hawaiian_Pidgin#/media/File:Ha...
> if it is God’s will (literally, “if God has willed [it]”
>In sarcastic contexts, it suggests that the speaker has no interest in making the future event occur (thus, it will only occur if God steps in and wills it). Unlike the Arabic usage, this seems to be more attested in English than the literal meaning.
I've heard it used in terms of avoiding the evil eye.