Cousins
First, please note the term "removed" is in no way meaning "less related to".
You have more common ancestors to your mother's cousin, (your first cousin, once removed) than your second cousin (your mother's cousin's children).   "Removed" simply means, removed a generation level.
Another example of a first cousin, once removed would be your first cousin's child.
Twice removed means that there is a two-generation difference. You are two generations younger your grandmother's first cousin. So you and your grandmother's first cousin are first cousins, twice removed.

To find cousins on your generation level:
- Your First cousins and you share a grandparent as the closest ancestor.
- Your Second cousins and you share a common great grandparent as the closest ancestor.
- Your Third cousins and you share a common great, great grandparent as the closest ancestor, and so on...
These cousins are important because they are on the same generation level as you and are likely still living
(although can vary greatly on age depending on birth order of ancestors).  These living cousins, no matter how distant, may have valuable information on common ancestors. As I have found.

Double cousins occur when two brothers of one family marry two sisters of another family, and both
marriages produce children.  These children are double first cousins.
An example occurs in this database (you will need to be logged in previously to view the example).  You will see in this example the same cousins listed in the maternal and paternal side.  This is not an error, rather an indication of double cousins.

Although no examples of cousins marrying cousins have yet to be found in this database, married cousins of some level exist (whether it be second, third, fourth...tenth cousins marrying).  An ancestor of yours born in the 1800s could have produced thousands of 7th cousins of yours.  Obviously, if you go back far enough with any stranger on the street, you would find a common ancestor. (if all lineage of all persons were known.)  Only a few generations back, travel was limited, and people seldom traveled outside a small radius of where they lived. If you go back 20 generations (around the 1500s), you would have over a million family surnames.  Go back 33 generations (around the year 1250), and you would statistically have more than 8.5 billion surnames - way more than the population of the earth (even currently)!  Obviously cousins, of whatever distance, do marry.
Interestingly, if a third cousin married another third cousin, that child would be it's own double fourth cousin as well!
(and the child would also be the third cousin, once removed to both the parents)

                                          Relationship Chart

                                4 X Great
                               Grandparents
                                 /      \
                          3 X Great    4 X Great
                       Grandparents    Uncle-Aunt
                           /     \            \
                    2 X Great   3 X Great   1st Cousin
                  Grandparents  Uncle-Aunt  4 X Removed
                     /     \            \           \
               Great     2 X Great    1st Cousin   2nd Cousin
           Grandparents  Uncle-Aunt   3 X Removed  3 X Removed
               /     \           \            \           \
         Grand      Great       1st Cousin   2nd Cousin   3rd Cousin
        Parents   Uncle-Aunt    2 X Removed  2 X Removed  2 X Removed
         /     \           \            \           \           \
   Father     Uncle   1st Cousin    2nd Cousin    3rd Cousin    4th Cousin
   Mother     Aunt    Once Removed  Once Removed  Once Removed  Once Removed
   /     \           \           \            \           \           \
ME      Brother       1st          2nd         3rd         4th          5th
         Sister      Cousin       Cousin      Cousin      Cousin       Cousin
   \           \           \            \           \           \
    Son     Nephew   1st Cousin    2nd Cousin    3rd Cousin    4th Cousin
  Daughter   Niece   Once Removed  Once Removed  Once Removed  Once Removed
         \           \           \            \           \
         Grand      Grand       1st Cousin  2nd Cousin  3rd Cousin
         Child  Nephew-Niece   2 X Removed  2 X Removed 2 X Removed
               \           \            \           \
              Great    Great Grand   1st Cousin  2nd Cousin
           Grandchild  Nephew-Niece  3 X Removed 3 X Removed
                     \           \            \
                  2 X Great  2 X Great Grand  1st Cousin
                 Grandchild   Nephew-Niece    4 X Removed
                           \            \
                        3 X Great  3 X Great Grand
                         Grandchild   Nephew-Niece
                                 \
                              4 X Great
                              Grandchild

The diagonal ascending lines are the parents and the diagonal descending lines are the children. For example, if you have the same Great-Great Grandparents as someone, you are 3rd cousins. If  your Great Grandfather is his Great Great Great (3 X) Grandfather, you are second cousins, twice removed (2 X).
The chart above can be extended to the upper right and lower right as far as desired for whatever degree of cousin you want.  The term "Great Uncle" is actually your "Grand Uncle" in genealogical terms.