Relay states and NO vs NC contacts. Lights on board status - what gives?

I’m really confused and hoping someone can explain the relays to me.
Here’s what I see in my testing.
Hardware: Arduino Uno (same results with Nano), Songle SRD-05VDV-SL-C relay
Software: Only asking to turn on and off (to test):
void RelayOneOn(){
// Turn relay on
digitalWrite(RelayOne, HIGH);
Serial.print(“Relay ON”);
}

void RelayOneOff(){
// Turn relay off
digitalWrite(RelayOne, LOW);
Serial.println(" Relay OFF");
}

Results with multimeter:
Relay not connected (no wires, no power):
NO, C , NC; on board LED light is off (duh)
Resistance testing:
NO - no connection
NC - connected

Relay connected to power, but NOT switched at all:
NO, C , NC; on board LED light is on
Resistance testing:
NO - is connected
NC - not connected

Relay connected to power, AND switched OFF:
NO, C , NC; on board LED light is ON
Resistance testing:
NO - IS CONNECTED
NC - NOT connected

Relay connected to power, AND switched ON:
NO, C , NC; on board LED light is OFF
Resistance testing:
NO - NO CONNECTED
NC - IS connected

This is opposite of what I would expect. I assume:
if relay is either no powered or powered: the NO circuit would be unconnected and on board LED off
If relay is powered, but not switched on: the NO circuit would be unconnected and on board LED off
If relay is powered, and switched on: the NO circuit would be connected and on board LED on

Do I have the understanding correct? Am I really way off?
I can’t find any information on this on-line that talks about the various states.
My project works, but in reverse of what I want. Worst of all, if I take away the power, the relays allow power to the circuit to be ON. Not what I want.

Oh, and my relays do NOT have NO,C,NC indicators so assuming left to right: NO, C, NC
These are the symbols looking at the relay:
| | |
|_ \ _|
NO C NC

Please educate me on this. Thank you.

NC and NO refer to the condition of the contacts with no power applied to the coil i.e. you holding the relay in your hand.

If there is a LED cct. across the coil and this LED is on (there is coil voltage) and the voltage is = to the relay rated coil voltage, the NO contact should close and the NC contact should open.

Some relays are of the latching type.

Also some suppliers of the Chinese derivative relay modules may mark NO and NC incorrectly.

In which case LED lit may mean either NC or NO so ALWAYS check which is true.
I have some here that are marked in that manner :o

Sounds like your relay is the typical opto isolated type that are "LOW TRUE" , they are energized when the input pin is grounded (LOW) and OFF when the pin is HIGH. Program something like this:

const byte relayPin = 4;
void setup()
{
  digatalWrite(relayPin, HIGH); // make sure relay pin is HIGH (OFF) at startup
  pinMode(relayPin,OUTPUT); // relay pin is set as OUTPUT but is turned OFF

}
void loop()
{
 digitalWrite(relayPin, LOW); // turn the relay ON    NO----COM    NC
 delay(2000);                 // wait 2 seconds
 digitalWrite(relayPin, HIGH); // turn the relay OFF  NO    COM----NC
 delay (4000);                 // wait 4 seconds
}

When working with digital logic, get the idea that HIGH is ON and LOW is OFF out of your mind, it will only confuse. HIGH can be EITHER ON OR OFF, depending on hardware.