OSCommerce tep_db_input vs tep_db_prepare_input

I am working on a project that uses OSCommerce with MySQL and I'm confused as to when I should use tep_db_input() or tep_db_prepare_input(). I'd assume I should use tep_db_input() around any strings that are being inserted/updated, but then when should the other function be used?

For example, if I were to SELECT some data from the database, and use the result to then INSERT a row into another table, do I need to prepare the input at some point? Or just use tep_db_input again?

$width = '3"'; // 3 inches
$new_height = '3\' 5"'; // 3 feet 5 inches

$result = tep_db_query(
    "SELECT height 
     FROM measurements 
     WHERE width = '".tep_db_input($width)."'"
);

while ($row = tep_db_fetch_array($result)) {
    tep_db_query(
        "INSERT INTO measurement_history (
            field, 
            old_value, 
            new_value
        ) VALUES (
            'height',
            '".tep_db_input($row['height'])."',
            '".tep_db_input($new_height)."'
        )"
    );
}

Is this correct?

Edit:: In case anyone isn't familiar with those functions, here are their definitions:

function tep_sanitize_string($string) {
    $patterns = array ('/ +/','/[<>]/');
    $replace = array (' ', '_');
    return preg_replace($patterns, $replace, trim($string));
}

function tep_db_input($string, $link = 'db_link') {
    global $$link;

    if (function_exists('mysql_real_escape_string')) {
        return mysql_real_escape_string($string, $$link);
    } elseif (function_exists('mysql_escape_string')) {
        return mysql_escape_string($string);
    }

    return addslashes($string);
}

function tep_db_prepare_input($string) {
    if (is_string($string)) {
        return trim(tep_sanitize_string(stripslashes($string)));
    } elseif (is_array($string)) {
        reset($string);
        while (list($key, $value) = each($string)) {
            $string[$key] = tep_db_