man bash
says:
Shell Function Definitions
A shell function is an object that is called like a simple command and exe‐
cutes a compound command with a new set of positional parameters. Shell
functions are declared as follows:
name () compound-command [redirection]
function name [()] compound-command [redirection]
This defines a function named name. The reserved word function is
optional. If the function reserved word is supplied, the parentheses
are optional. The body of the function is the compound command com‐
pound-command (see Compound Commands above). That command is usually
a list of commands between { and }, but may be any command listed
under Compound Commands above. compound-command is executed whenever
name is specified as the name of a simple command. When in posix
mode, name may not be the name of one of the POSIX special builtins.
Any redirections (see REDIRECTION below) specified when a function is
defined are performed when the function is executed. The exit status
of a function definition is zero unless a syntax error occurs or a
readonly function with the same name already exists. When executed,
the exit status of a function is the exit status of the last command
executed in the body. (See FUNCTIONS below.)
In short, no there is no difference.
name() {...}
is POSIX, and more universal. Since all notations accomplish the same thing, I prefer to use the most portable (universal) notation as specified by POSIX. – RobertL Dec 04 '15 at 03:38