The examples are from Dave Weigert's "Workshop for bass and drums - How to play in bands" book, one of the authoritative sources, I'd say.
The thing is, both examples are shown as examples of Non-Specific Notation. Basically, it is up to you to interpret it on the instrument.
One way I interpret the instruction about the rhythm slashes is - the first case is specific, so play only the rhythm syncopated as indicated. In the second case, play time that accompanies the rhythm indicated above the bar lines, while also syncopating the indicated rhythm (i.e. perhaps, first note accented a bass drum, next with the snare, then cymbal, etc., all while playing regular time).
Think about it this way - listening to that piece (without drums), what would you play had you not seen the notes chart?
That said, if you have the book, check the lead sheet for Nardis, for example. It contains the notation from the first example, where you're expected to play just the rhythmic figure. The exact drum sound is not indicated. Play it on cymbals, hi-hat, with brushes, on the rim, clapping hands, whatever you find appropriate.
In all the sheets in the book, I have not seen the use of the second notation style.
You can check Tony Williams' interpretation or Bill Evans' version. Here you can hear that the syncops are played along with time. Note that the ensemble comes in only after ~4-5 minutes of Bill's intro.
In the end, I would reiterate the words: "Jazz in an aural tradition that should be learned primarily through listening, not reading."