Here is the specs for comparison. I agree that all three tubes are similar, but believe they were each designed individually and none is taken from the other. Look at the mechanical construction and one can see that the 6V6 plate would not fit either of the other two envelopes. Likewise the 6P1P/-EV would not fit in the 6AQ5 envelope.
Both the 6AQ5 and 6V6 have much higher max Ik as both were designed for vertical deflection service as well as to be used for audio output.
The 6AQ5 is a beam power pentode, the 6V6 is a a beam power pentode, and the 6P1P/-EV are Tetrodes with the characteristic kink in the plate curves.
6P1P 6P1P-EV 6AQ5 6V6
Va 250 250 275 315 V
Vg2 250 250 275 315 V
PD 12 na 12 na 12 10 12 9 W Pent/Tri
G2D 2.5 1.3 2 2 mA
Ik 70 70 115 105 mA
Rp 42500 57500 58K 52K 50K 50K R
Gm 4900 4900 3700 4700 3700 4100 uMho
Cg1k 8 7.5 8.5 9 pf
Cak 5 4.5 8 7.5 pf
cg1a 0.9 0.7 0.4 0.7 pf
0Vbias, 200VAk 83 83 93 90 mA
20Vbias, 300Vak 38 38 42 40
Distortion <=14% 8%
From Curves 4.8W 5.5K 6% 5.2S 5.5K 8.5% 4.75 5.5K 7.6% 5W 6K 6.5%
Ia at distortion min 55mA 55mA 45mA 47mA
Sorry about the chart. I'll post a screenshot when I get home. I can't link pix at work.