Basically when calibrating the monitor I have no technical knowledge of what exactly is happening, so can you please explain the process in simple terms?
Let me give you part of the answer now and before I start, just know that I'm anthropomorphising a bit to explain it simply. Also, I spell Colour as Color because my iPad speaks American English and I hate those red underlines it shows under 'misspelled' words if I don't conform.
The calibration tool will tell your computer to show a particular set of colors at particular brightness on the monitor and then will measure those particular colors to see if they match its request.
Let's say, hypothetically that the calibration tool tells the system to have the monitor display 660 nm wavelength (Red). However, the monitor displays only 640 nm, even though the computer 'thinks' it's displaying 660 nm on the monitor. The calibration hardware resting on the monitor is expecting to see 660 nm, but notices it's closer to 640 nm.
When this happens to my system, my calibration tools say "Shaw's computer is drunk. Again. I'll make a note of this in a record (a table) to let the computer 'know' it's off by about 20 nm at this color red."
Then the calibration tool measures a few other colors and records all of this in a multidimensional table and a few tone response curves. The table and tone curves will be used by the computer to look up which values should be used to show which colors. For example it might list that the computer must push the red diodes a bit harder than it did before to show 660 nm. This table, these tone response curves, and a few other things are recorded in a file. This file is called an ICC profile.
Why is it called an ICC profile? I'm not sure, but I believe it's because the engineers at the International Color Consortium (ICC) couldn't think of a more creative name.
Now that you know the basics, there are a few other items I should mention just so you know and also before someone else reading this gets huffy and shouts, "Shaw! Why did't you mention 'Tristimulous values', why didn't you tell him that Spectrophotometers are better than Colorimeters, why didn't you mention the importance of the illuminant, D65 vs. D50, yada, yada, yada ".
So they don't get up-in-arms, here you go ...
your Spider is a Colorimeter and is perfectly adequate for your monitor (or any other self-luminous object). Spectrophotometers have more fidelity, very appropriate if you are working in the print, paint or coating industry. You don't need one now.
Use D65. Unless your set up is for professional printing workflow, then you'll use D50 ... sometimes. But you aren't, so use D65.
When you are using the OSD and the predefined profiles, you are selecting a different ICC profile than your recently calibrated custom ICC profile.
Although you didn't ask, you should know Photoshop handles color a little differently than other applications, so make sure you look at your image outside of Photoshop to gauge the colors
Also, since you are getting serious about color, consider working in Lab color mode when you're editing in Photoshop.
I'm running out time at the moment so I may return to complete this answer, but I bet that someone else will beat me to the punch...
Edit 2014/12/09 - From your comments, it looks like you have multiple profiles and that the computer's configuration, set-up, and/or system-state influence which profile is enabled. As such, I am not in the best position to assist because I can only guess at your configuration. Nonetheless, if I were in your shoes, I would eliminate variables until you can identify the causes. For example, as a test, I would carefully disable the LG software used to manage profiles, and use only the Spider software to create and manage profiles. If the profile is retained when you cycle off-and-on, then you've identified the culprit.