That is correct and a little info here might help some in understanding these 2 relay circuits.
The low voltage , on/off circuit you talk of is the primary side of the relay [any relay].. this is simply the relay coil/solinoid that pulls in the secondary contacts [ in this case , high amps vs volts, as both primary and secondary are 12v.]
So, the sensors are on this primary circuit and they simply complete the circuit [usually to ground]. The thing to look into on this side of the relay is that there is also a power feed [ 12 v pos] that is fused to the fuse box.. so if this feed fuse is open, no fan circuit..
The actual high amp contacts in the relay are the secondary section/circuit.. this circuit simply feeds power to the fans.. this side is also fused and called the LOAD side ..
So, what we have here is a dual fan circuit -low/ac and high/ eng temp activated with , get this, 4 fuses... feed fuses for both relay coils side and load fuses for fan amp draw on secondary contacts..
The most common fuse problem will be , of course, on the LOAD side as this is the high amp draw circuit. , But , it is possible to have a coil side power fuse blown [ these are usaully in the main fuse box and coupled up with other circuits]
One of the test I do when jumpering a high side a/c switch to
test the low fan circuit [ and this test checks the entire circuits integrity, except the pressure sw itself] , is to listen up near the relay locations for an audible Click from the relay coil.. it can be faint, but this will tell you that you have primary coil feed to the relay and now one knows that the problem has to be on the secondary part of the circuit.... ie.- load fuse , dropping resistor, fan motor, etc,,,