Answer 1

array_map has no collateral effects while array_walk can; in particular, array_map never changes its arguments.
array_map cannot operate with the array keys, array_walk can.
array_map returns an array, array_walk only returns true/false. Hence, if you don't want to create an array as a result of traversing one array, you should use array_walk.
array_map also can receive an arbitrary number of arrays, while array_walk operates only on one.
array_walk can receive an extra arbitrary parameter to pass to the callback. This mostly irrelevant since PHP 5.3 (when anonymous functions were introduced).
The resulting array of array_map/array_walk has the same number of elements as the argument(s); array_filter picks only a subset of the elements of the array according to a filtering function. It does preserve the keys.

Example:

<pre>
<?php

$origarray1 = array(2.4, 2.6, 3.5);
$origarray2 = array(2.4, 2.6, 3.5);

print_r(array_map('floor', $origarray1)); // $origarray1 stays the same

// changes $origarray2
array_walk($origarray2, function (&$v, $k) { $v = floor($v); });
print_r($origarray2);

// this is a more proper use of array_walk
array_walk($origarray1, function ($v, $k) { echo "$k => $v", "\n"; });

// array_map accepts several arrays
print_r(
array_map(function ($a, $b) { return $a * $b; }, $origarray1, $origarray2)
);

// select only elements that are > 2.5
print_r(
array_filter($origarray1, function ($a) { return $a > 2.5; })
);

?>
</pre>

Result:

Array
(
[0] => 2
[1] => 2
[2] => 3
)
Array
(
[0] => 2
[1] => 2
[2] => 3
)
0 => 2.4
1 => 2.6
2 => 3.5
Array
(
[0] => 4.8
[1] => 5.2
[2] => 10.5
)
Array
(
[1] => 2.6
[2] => 3.5
)