user14960: I am new to electronics and Arduino.
What is the difference between power supply ground and Arduino's ground. If I connect my LED cathode to power ground, it doesn't work. But if I connect it to Arduino ground, it works. Aren't all ground the same? 
Please see picture below.


user14948: I agree with the other answers.  On rare occasions, TO-xxx packages have bizarre pinouts, but the 78xx series does, in fact, have ground on the middle terminal.  This is surely a split power supply in your breadboard power busses, or else a bad breadboard.  Many breadboards have splits in the power rails halfway down.  I've also seen some with splits more often than that, perhaps as much as disconnects every 5 (or 5 pairs of) contacts.  I have a breadboard, for example, which allows for 6 different voltages, all in a single line, from various connections to a battery pack.  I'd recommend buzzing the breadboard before starting to use it.  
I've also had breadboards whose contacts fail after using larger AWG wires in particular holes (or forcing odd connections, such as machined contacts on IC's or sockets, or larger stamped rectangular pins on a TO package such as this) into breadboard holes. The last thing you want to worry about when building a prototype of a new design is whether or not the wiring under the breadboard works.
Many multimeters have a continuity test capability for diagnosing problems such as these, BUT make sure no power is connected (or you could damage the meter on this setting).

user10907: I would expect there to be no difference between the grounds in your circuit, and after looking over the schematic for the board, it appears that all of the grounds are common.
I think the most likely explanation for what you're seeing is a quirk in the breadboard. It may be that the side busses are split at the middle of the board, or perhaps there was just a bad connection somewhere on the ground bus on that side of the board.
One way you could troubleshoot it further would be by jumping the ground side of the LED to the power supply ground. Start with the ground on the regulator and then work out until you find the spot where you loose continuity.

14960: <p>I am new to electronics and Arduino.</p>

<p>What is the difference between power supply ground and Arduino's ground. If I connect my LED cathode to power ground, it doesn't work. But if I connect it to Arduino ground, it works. Aren't all ground the same? </p>

<p>Please see picture below.</p>

<p><a href="https://i.stack.imgur.com/AhDtD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/AhDtD.png" alt="enter image description here"></a></p>
 14948: <p>I agree with the other answers.  On rare occasions, TO-xxx packages have bizarre pinouts, but the 78xx series does, in fact, have ground on the middle terminal.  This is surely a split power supply in your breadboard power busses, or else a bad breadboard.  Many breadboards have splits in the power rails halfway down.  I've also seen some with splits more often than that, perhaps as much as disconnects every 5 (or 5 pairs of) contacts.  I have a breadboard, for example, which allows for 6 different voltages, all in a single line, from various connections to a battery pack.  I'd recommend buzzing the breadboard before starting to use it.  </p>

<p>I've also had breadboards whose contacts fail after using larger AWG wires in particular holes (or forcing odd connections, such as machined contacts on IC's or sockets, or larger stamped rectangular pins on a TO package such as this) into breadboard holes. The last thing you want to worry about when building a prototype of a new design is whether or not the wiring under the breadboard works.</p>

<p>Many multimeters have a continuity test capability for diagnosing problems such as these, BUT make sure no power is connected (or you could damage the meter on this setting).</p>
 10907: <p>I would expect there to be no difference between the grounds in your circuit, and after looking over the <a href="https://www.adafruit.com/images/product-files/2377/Arduino-Pro-Mini-v14.pdf" rel="nofollow">schematic for the board</a>, it appears that all of the grounds are common.</p>

<p>I think the most likely explanation for what you're seeing is a quirk in the breadboard. It may be that the side busses are split at the middle of the board, or perhaps there was just a bad connection somewhere on the ground bus on that side of the board.</p>

<p>One way you could troubleshoot it further would be by jumping the ground side of the LED to the power supply ground. Start with the ground on the regulator and then work out until you find the spot where you loose continuity.</p>
