Technically, anytime you share more than one line you can be called a double cousin. My paternal tree is chock full of cousins with more than one family. It just isn't a joke when I say I am related to half of Santa Rosa and Escambia counties. That said, when I use that term I refer specifically to one set of circumstances alone. A double cousin is when you have a pair of siblings marry another pair of siblings. In my case, my great grandfather's sister married the brother of his wife.
So how does that affect DNA? Well looking at the ISOGG table, a first cousin would normally share 12.5 percent of DNA. Children of the double cousin marriage would share an average of 25 percent DNA. They also have the potential to have full and not half DNA matches.
Because I have tested both my father and his sister, and we have matches available who are double cousins, and multiple cousins, I am going to illustrate a difference in the shared DNA totals.
First let's take a look at CP. CP is the half first cousin once removed of my father and his sister, but CP is also their third cousin from another family. I haven't identified the segments for CP with my Aunt yet, but my father shares DNA from both families with her.
A half first cousin once removed has an estimation of sharing 3.125 percent of their DNA or 212.5 cM and a third cousin has the estimation of sharing 0.78 percent or 53.13 cM. Now we know it really should be a range, and that it is possible to share more or less with a match. So how does CP compare with my Aunt and my Dad? An average would be 265.6 cM. Dad shares 209.6 cM and his sister shares 361.5.
Next look at a double cousin. (I have several who have tested but results aren't available for both siblings). The first double cousin, DB is available to compare to both my dad and his sister. DB is a second cousin once removed from my Dad. The table shows double second cousins at 6.25 percent, so they should share 3.125 percent or about 212.5 cM. DB shares 370 cM with my Dad (220 cM with me!) and 215 cM with my Aunt.
The next double cousin is a first cousin of DB and is on Ancestry. DF shares 150 cM with me and 222 cM with my Aunt. Dad has two more on 23andme, sisters, they are also 2nd cousins once removed from a different child of the double cousin connection. One shares 4.58 percent, the other shares 2.81 percent. (23 and me gives percentage only, one is above the 3.125 average, one is below).
So let's look at another multiple cousin grouping from Dad's McCurdy line. So we have two sets of multiples to look at. The first is my Dad's great grandmother's sister who married her first cousin. Now I am not sure I am competent enough to tell you how much DNA they should share but, it is more than the normal relationship. We have a plethera of testers now from this branch, but let's look at two, granddaughters of Carrie McCurdy and Jack. PM shares 168.9 cM with Dad and 193 cM with my Aunt, both of them are 2nd cousins once removed (average 106 cM). CM shares 107 cM with Dad and 187 cM with my Aunt. I have left off the X DNA matches in the total, they are 39.9 and 18 for Dad (PM and CM) and 36.9 and 19.6 for his sister. (Actually they are second cousins once removed and third cousins once removed).
Let's look at scenario number two. These are grandchildren of Dad's great great grandfather and his second wife, who happened to be his great niece. So they are half 2nd cousins twice removed on one side, and full fourth cousins on the other. ( I know it's complicated). JW shares 73 autosomal and 28.2 X cM with Dad, his first cousin JM shares 103 autosomal and 33 X cM with Dad. JW shares 122 autosomal and 28 X cM with my Aunt, his first cousin JM shares 108.9 Autosomal and no X with her.
So even when you share multiple lines, you may not share "more" DNA but you can share DNA from multiple lines, but if you are a "double" cousin, well, you will share a lot of DNA. So what is the difference? Double cousins share four not two grandparents in common, and I think that that's what makes the biggest difference, aside from genetic distance in generations in how much you share with a multiple cousin.
Hope this helps!