I think you're overthinking the difference between using arrows (upper schematic) and the more common + / - signs and ground symbols (lower schematic). Basically they're different ways of indicating the same thing, a voltage and it's polarity.
However in the upper schematic with the arrows, it is undefined what connects to "ground level potential. All voltages are referenced to the line connecting to the + input of the opamp but nothing says that the voltage on that line is the ground reference. In the bottom schematic that is indicated clearly with the ground symbols.
The "e" in the bottom schematic is confusing and it is not following conventions, it has no + and - so I cannot see what "e" means.
Yes the circuits are the same.
To "easily" understand that there must be a minus sign in the transfer, you must realize that the opamp will steer it's output such that the voltage difference between its (+ and -) inputs is zero. That means that the opamp forces the voltage at the - input to be zero (because the + input connects to ground so it is zero volt by definition).
Knowing that, now work put what the output will be when the input has a positive voltage. Z1 and Z2 work as a voltage divider so the voltage at the output of the opamp must become negative to satisfy the zero volt at the - input.
Learn more by reading Opamps for Everyone.