A crude but effective analogy : Think about sailing a log vs a door. one will probably "go" (??) sooner, but the other will be rideable once it does "go".
No, it's a lot more than width. But width is one of the most significant influencers in planing thresholds (especially in these size/style of boards). Another is volume. And the respective rockerlines of the boards in comparison (a flatter rocker in any volume will help early planing, but more often not top end control or manoeuvrability). And even rail shape (softer rails planing later than hard, deep ones). Another simplistic (in an otherwise complex set of variables) can be even fin size and type - simply changing a dodgy 34cm freeride fin to a good quality 34cm race fin can do wonders for early planing/marginal conditions performance.
Typically, with minimal rider input*, a higher volume board of equal width (so thicker) will plane earlier (simply because ultimately the extra displacement helps get the board to rise to planing condition earlier. But (in modern freeride designs), it's fairly well established that thicker boards don't ride/control so well at high/er speeds, so the trade off is that the use of (extra) width delivers more benefits in the "early planing vs top end control" vs more/higher volume on narrower width.
That optimum ratio is not fixed, rather will vary for boards designed for different conditions/operating speeds/wind+sail range and the zillion other variables..
Those variables, like water and wind condition (choppy, rough water and patchy, gusty wind usually makes pumping a board to the plane more difficult - and thus favors volume - at least at the critical "getting (keeping) planing" transition). Sail type and tuning (for example - and not limited to -comparitive downhaul/outhaul settings on 6.5 vs 7.3m could iinfluence/ advantage marginal planing threshold - albeit at expense of top end speed/control).
*Rider input is a significant variable in this discussion - especially in this 111-122lt+6.6m-7.5m range - as typically these sizes are commonly used in/around planing threshold conditions and at critical planing thresholds, a skilled/energetic/determined rider could most likely pump his C111/7.3m to the plane ahead of a static (no active input) rider with C122/6.5m (everything else being equal, and in reality, it never is..)
Getting that board moving forward (earlier) by any means possible (ie pumping) allows the use of lower volume for equivalent planing threshold.
That's the short form version of an otherwise long and complex discussion -and, umm, well, it IS truly sunny and windy and I need to test some doors
Cheers ~ Ian