Short answer: No, there are no differences. Quotation marks are removed during parsing.
In the "Assigning Variables" section of a POSIX link :
In the shell command language, a word consists of the following parts:
varname=value
and a few lines below, you will see:
If no value is specified, the variable is assigned an empty value.
To check this (in Bash):
$ variable1=
$ variable2=''
$ declare -p variable{1,2}
declare -- variable1=""
declare -- variable2=""
they look the same!
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