Hi
About the schematics:
The one shows
* a battery
* no GND node
The other just shows:
* A, B, V, OUT and a GND symbol.
In this case when one talks about "V" or "V voltage" ... without any other information, one expects the voltage is referenced to GND.
An example: Let´s say V = 5V, A = 4.5V, B = 0.5V ...
* then "V = 5V" means "V referenced to GND = 5V"
* the same is with A and B.
* if you want to say it the more exact, but also more complicated way, then you may say "A to GND voltage" or "A-GND voltage".
* but in case you don´t want to refer to GND you may say "A-B voltage", which means "Voltage_A_referenced_to_GND minus Voltage_B_referenced_to_GND" which is: 4.5V - 0.5V = 4.0V
***
Indeed the "V" in your circuit can be misleading.
In your case it just names the node. But often it is used as abbreviation for "Volts". Thus try to avoid V as name.
In datasheets you often may find V_AB ... which means "Voltage of node A referenced to node B"
Like at MOSFETs: There is Gate = G, Source = S. .... and when they talk about V_GS the mean the voltage of Gate referenced to the voltage of Source.
Klaus