In general 1.e4 b6!? is the Owen defence whilst 1.d4 e6 2.c4 b6!? or 1.d4 b6!? 2.c4 e6 or 1.c4 b6!? 2.d4 e6 is the English defence (tough the Owen could transposes to the English, e.g. 1.e4 b6!? is the Owen but after 2.d4 Bb7 3. Bd3 e6 4.c4!? is already a position from the English defence). The pure Hippo set-up could be obtained from either of theme. Finally, the Hippo is more set-up than a defence. According to it's pawn structure in ideal the Hippo should transposes to a kind of Benoni (or even Hedgehog)  after the...c7-c5! strike (the most common and important strike in the Hippo) though other strikes (for example the ...f7-f5 strike as in the above game Kempinski, R. (2590) vs. McShane, L. (2614)) are also very common.

Regards,

Nick

If White doesn't play c2-c4 then it's an Owen.

Exactly - If White doesn't play an early c2-c4 then it's an Owen defence.