Two leaf stage in most writing, including mine, means cotyledons, usually long and thin, except mainly for rounder brassicas. Then the third leaf is the first true leaf of more variable shape and size. I find that pricking out at cotyledon stage is easy and effective. It is still possible with bigger seedlings but takes longer and they are a little more shocked by the move.
Moon planting and sowing is tricky, there are so many variables, as outlined for example by Maria Thun – and she barely considers waxing and waning! I am running several experiments and the results are quite variable, perhaps because there are so many other variables, not least at this time of year the fast-waning season i.e. each day waiting to sow, beyond the optimal time (such as now in Britain for lambs lettuce, spring onions, spring cabbage) is important time lost and if you wait too long for an ideal moon, whichever that is, then plants may not be large enough to either crop or survive through winter. So in late summer and autumn I pay more attention to seasonal times than considerations of moon. With an exception that 11th September this year is two days before full moon!! and I shall sow lettuce, endive, oriental leaves etc for winter salad in my polytunnels….