I agree with your translation of the sentence.  I would understand the sentence as you do.

And for the YTD (Year To Date), how you differ from the "as of"? I imagine I must use the YTD when the data is from a certain date up to the present moment.

"As of" requires a point of reference.  Perhaps it's only implied, but there must be a date/time.  When you wrote "from a given date", you were talking about a point of reference, the beginning of a time period.

"As of the second of July, we had three mortal accidents."  Where is the point of reference?  Did the mine/factory start in February?  If it did and I knew it, I'd say you are telling me that since February there have been three deaths.  In YTD, the reference point if given:  the first of the year.  If you tell me "As of the

second of July, we had three mortal accidents" without a reference point, the information is of little use to me.  I don't know if you are talking about since the first of July, the 15th of March, since the mine/factory opened in 1958, or what.