I believe in the old days, PPS (i.e. 4 < k < 1200) was searched in chunks in an uneven way such that small k were advanced further than large k. This makes sense in many ways, but is hard to manage. The lowest k values reached megaprime domain in PPS, while the other k were far from reaching megaprimes.
The MEGA project was created starting just over the megaprime level (except k that were past that). And the PPSE was created doing small n in 1200 < k < 10000 instead, is you said. A new philosophy was initiated at PPS to try to have a "straight" leading edge, where all k are at the same n simultaneously.
MEGA was later moved to 1200 < k < 10000 to have many new candidates "just over" 10^999999.
It was realized that the new PPS philosophy was bad for Fermat divisor progress (setting low k on halt for several years), and therefore the DIV project was created to focus on 4 < k < 50 (and initially a couple of other magical k values, but those have been abandoned now). It is often forgotten that for two special k, namely k=9 and k=27, we are only considering odd exponents n in DIV. The even n for k=9 must wait; the even n for k=27 have been singly checked, see next paragraph.
For completeness, the multipliers k = 3, k = 27, and k = 121 have special subprojects, namely 321 (here on BOINC) and 27/121 (PRPNet), and in them, both +1 and -1 forms are searched. In 27/121, the double check is left to DIV (27, odd n, +1 form) and PPS (other +1 forms).