A command is split into an array of strings named arguments. Argument 0 is (normally) the command name, argument 1, the first element following the command, and so on. These arguments are sometimes called positional parameters.
$ ls -la /tmp /var/tmp
arg0 = ls
arg1 = -la
arg2 = /tmp
arg3 = /var/tmp
An option is a documented type of argument modifying the behavior of a command, e.g. -l commonly means "long", -v verbose. -lv are two options combined in a single argument. There are also long options like --verbose (see also Using getopts to process long and short command line options). As their name suggests, options are usually optional. There are however some commands with paradoxical "mandatory options".
$ ls -la /tmp /var/tmp
option1= -l
option2= -a
A parameter is an argument that provides information to either the command or one of its options, e.g. in -o file, file is the parameter of the -o option. Unlike options, whose possible values are hard coded in programs, parameters are usually not, so the user is free to use whatever string suits his/her needs. Should you need to pass a parameter that looks like an option but shouldn't be interpreted as such, you can separate it from the beginning of the command line with a double dash: --.
$ ls -la /tmp /var/tmp
parameter1= /tmp
parameter2= /var/tmp
$ ls -l -- -a
option1 = -l
parameter1 = -a
A shell parameter is anything that store a value in the context of the shell. This includes positional parameters (e.g. $1, $2...), variables (e.g. $foo, $bar...) and special character ones (e.g. $@)
Finally, there are subcommands, also known as functions / (low-level) commands, which are used with "metacommands" that embed multiple separate commands, like busybox, git, apt-get, openssl, and the likes. With them, you might have global options preceeding the subcommand, and subcommand specific options that follow the subcommand. Unlike parameters, the list of possible subcommands is hardcoded in the command itself. e.g.:
$ busybox ls -l
command = busybox
subcommand = ls
subcommand option1 = -l
$ git --git-dir=a.git --work-tree=b -C c status -s
command = git
command option1 = --git-dir=a.git
command option2 = --work-tree=b
command option3 = -C c
subcommand = status
subcommand option1 = -s
Note that some commands like test, tar, dd and find have more complex argument parsing syntax than the ones described previously and can have some or all of their arguments parsed as expressions, operands, keys and similar command specific components.
Note also that optional variable assignments and redirections, despite being processed by the shell for tilde expansion, parameter expansion, command substitution, arithmetic expansion, and quote removal like other command line parameters are not taken into account in my reply because they have disappeared when the command is actually called and passed its arguments.
