The music industry is basically comprised of two main functions.

    1) Making music - These would be labels or record companies. They hire artists and producers who make a tangible product to sell.

    2) Distributing music - These would be distribution companies. They might help promote the product and see that it gets shipped to stores.

Those making the music are responsible for hiring the people needed to make an end product - a record (or CD). They might sign an artist and hire a producer to over see the job of making a record/CD.

They partner up with the distributor once the product is completed and promote the record/CD. The distributor also has the infrastructure to deal with the record stores and outlets that will be selling the product to end users. It's in the best interest of the distributor for great sales as they share profits on sales with the record company.

Within these function are two more breakdowns - The major and the independent. 

Major players have their own distribution channels and often act as distribution channels for independent labels (Universal might distribute for Koch, for example). Some independents also have distribution channels and the lines between major and independent can be blurry sometimes. A major label might be part owner in a so-called independent label. Just look at the connections under the Universal label (partial list):

Universal
    - Interscope
       - Aftermath
          - Storchaveli
       - G-Unit
       - Shady records
    - Geffen
       - Flawless
       - DoggyStyle
       - Black Wall Street
    - Def Jam
    - Roc-A-Fella
    - So So Def
    - Machete (reggaeton)
       - Mas Flow
       - El Cartel
       - WY Records
   
So you can see the big fish is Universal and the fish get smaller at each level. You have all probably heard of Shady/Aftermath, Geffen/Interscope, etc. These pairings often refer to the label/distributor relationship. When a major label owns a peice of a lesser label, they are often the distributor or at least have their hands in the cookie jar.

Some people also believe that to be truly independent the label cannot be a member of the Recording Industry Association of America (RIAA)

The real difference in my opinion is simply that majors have tons of of money and the independent doesn't.

What this means is that while a major player can offer an artist:

    - More upfront money/budget (advance)
    - More money towards promotion
    - Better distribution channels
    - More pull at radio stations

An independent can offer:

    - Higher royalties (percentage-wise)
    - More artistic control

So which is better? None really. It depends on the goals of the artist. An artist selling less records might make more money on an independent label, but they might not get the world-wide exposure that a major could help with.

Of course, the full scope of the record industry goes much much deeper than what I've described here, but I hope you found this information useful and enlightening.