"Double Merle" vs "Homozygous Merle"
All double merles are homozygous merle. But not all homozygous merles are double merle. 

Double Merle Terminology

"Double Merle" is technically not a genetic term. We would never say "Double Sable" or "Double Black".
The terminology in the past has not only been used to describe a dog who is M/M - homozygous for the M allele, but more so refers to the white that can be created by the combination of two Merle alleles and the risk for hearing and/or vision impairments. This term can be referred to as a "descriptive term" rather than "genetic".   
Using the "langevin et al" scale with the alleles of m, Mc, Mc+, Ma, Ma+, M and Mh there are 28 possible merle alleles combinations.
14 of those combinations can delete pigment to white and come with either low, moderate or high risk for the deletion of pigment and possible hearing and/or vision impairments.

The following chart shows those "double merle" combinations and the risk associated for hearing and/or vision impairments. Low risk combinations are known to cause hearing impairments only and not eye impairments.

Homozygous Merle

Genetically the term "homozygous" is defined as "having two identical alleles of a particular gene or genes.".   In the case of merle since there are 6 different M* allele lengths "homozygous" refers to a dog having 2 M* alleles - although they may not be identical in length - as all the alleles are the exact same mutation. The different lengths alleles are only broken down into different allele lengths for breeding purposes - in this regard the alleles of Mc, Mc+, Ma, Ma+, M and Mh are "man-made" specifically for breeders. 

The following dogs are examples of "homozygous merles" but NOT  "double merles" as the allele combination cannot delete pigment to white.

Mh - Harlequin Merle

The Mh falls into a "grey" area as far as pigment deletion.  Mh can delete pigment to white but is neither homozygous merle or double merle.  There is a very low risk of hearing impairments from the Mh allele and at this time no confirmed cases of eye impairments.