grep returns a list. In scalar context (my $index = ... for example) a list returns the count of elements in the list. Writing my ($index) = ... makes $index the first member of a one element list and grep's return list is in list context so the first element of grep's list is assigned to the first element of the left hand side list - $index.

$_ is always an alias to each element in the list for grep, map and in a for loop (whatever you use as the loop variable is the alias in the case of a for loop). In the first case you provide a list of numbers: 0 .. $#coins (indexes into the array). In the second case you provide a list of elements - the elements of @coins.

grep's "second parameter" is always a list. You provided two different lists in your sample code. The range operator generates a list.

Note that most often grep expressions are written using a block: grep {$_ ne "fourthy"} @coins.