A short snippet of test case & it's output regarding WPML's behavior in wp_update_term() function. Relates to question in http://wpml.org/forums/topic/updating-a-term-with-wp_update_term-causes-a-new-translation-created/ .

test_case_output.txt

Inserted FI: Array
(
    [term_id] => 171
    [term_taxonomy_id] => 176
)

trid after FI: 121

Inserted EN: Array
(
    [term_id] => 172
    [term_taxonomy_id] => 177
)

** First versions of categories inserted **
wpdb->update is run. Updates: Array
(
    [trid] => 121
    [language_code] => en
    [source_language_code] => fi
)
 WHERE: Array
(
    [element_type] => tax_test_folder
    [element_id] => 177
)

icl_translations table:
Array
(
    [translation_id] => 408
    [element_type] => tax_test_folder
    [element_id] => 176
    [trid] => 121
    [language_code] => fi
    [source_language_code] =>
)

Array
(
    [translation_id] => 409
    [element_type] => tax_test_folder
    [element_id] => 177
    [trid] => 121
    [language_code] => en
    [source_language_code] => fi
)

End of icl_translations table.

** First versions of categories inserted and translations linked **
** Starting to update categories **

Updated EN: Array
(
    [term_id] => 172
    [term_taxonomy_id] => 177
)

icl_translations table after updated EN translation:
Array
(
    [translation_id] => 408
    [element_type] => tax_test_folder
    [element_id] => 176
    [trid] => 121
    [language_code] => fi
    [source_language_code] =>
)

Array
(
    [translation_id] => 410
    [element_type] => tax_test_folder
    [element_id] => 177
    [trid] => 122
    [language_code] => en
    [source_language_code] =>
)

End of icl_translations table.

Updated FI: Array
(
    [term_id] => 171
    [term_taxonomy_id] => 176
)

icl_translations table after updated FI translation:
Array
(
    [translation_id] => 411
    [element_type] => tax_test_folder
    [element_id] => 176
    [trid] => 123
    [language_code] => fi
    [source_language_code] =>
)

Array
(
    [translation_id] => 410
    [element_type] => tax_test_folder
    [element_id] => 177
    [trid] => 122
    [language_code] => en
    [source_language_code] =>
)

End of icl_translations table.

******** END OF TEST RUN ********

wpml_term_update_test.php

<?php
  global $sitepress; global $wpdb;
	
	$taxonomy = 'test_folder';
	$primaryLanguage = 'fi';
	
	// First inserting Finnish category
	$_POST['icl_tax_' . $taxonomy . '_language'] = $primaryLanguage; // WPML
	$inserted = wp_insert_term("Category in Finnish", $taxonomy, array());
	echo "Inserted FI: ".print_r($inserted,true)."\n\n";
	
	// Saving Finnish category details + WPML $trid to variables
	$fi_term_id = $inserted['term_id'];
	$fi_tt_id = $inserted['term_taxonomy_id'];
	$trid = $sitepress->get_element_trid($fi_tt_id, 'tax_' . $taxonomy);
	echo "trid after FI: $trid\n\n";
	
	// Then inserting English category
	$_POST['icl_tax_' . $taxonomy . '_language'] = 'en'; // WPML
	$inserted = wp_insert_term("Category in English", $taxonomy, array());
	echo "Inserted EN: ".print_r($inserted,true)."\n\n";
	
	// Saving English category details
	$en_term_id = $inserted['term_id'];
	$en_tt_id = $inserted['term_taxonomy_id'];
	
	echo "** First versions of categories inserted **\n";
	
	// Linking English translation to Finnish translation
	$updates = array('trid' => $trid, 'language_code' => 'en', 'source_language_code' => $primaryLanguage);
	$where = array('element_type' => 'tax_' . $taxonomy, 'element_id' => $en_tt_id);
	$wpdb->update($wpdb->prefix . 'icl_translations', $updates, $where);
	
	echo "wpdb->update is run. Updates: " . print_r($updates,true)." WHERE: " . print_r($where,true)."\n";
	
	echo "icl_translations table:\n";
	$icl_translations = $wpdb->get_results("SELECT * FROM {$wpdb->prefix}icl_translations WHERE element_type = 'tax_" . $taxonomy . "'", ARRAY_A);
	foreach ($icl_translations as $row) {
		print_r($row);
		echo "\n";
	}
	echo "End of icl_translations table.\n\n";
	
	echo "** First versions of categories inserted and translations linked **\n";
	echo "** Starting to update categories **\n\n";
	
	// Updating the English category
	$_POST['icl_tax_' . $taxonomy . '_language'] = 'en'; // WPML
	$updated = wp_update_term($en_term_id, $taxonomy, array('name' => 'Category in English, updated'));
	echo "Updated EN: ".print_r($updated,true)."\n";
	
	echo "icl_translations table after updated EN translation:\n";
	$icl_translations = $wpdb->get_results("SELECT * FROM {$wpdb->prefix}icl_translations WHERE element_type = 'tax_" . $taxonomy . "'", ARRAY_A);
	foreach ($icl_translations as $row) {
		print_r($row);
		echo "\n";
	}
	echo "End of icl_translations table.\n\n";
	
	// Updating the Finnish category
	$_POST['icl_tax_' . $taxonomy . '_language'] = 'fi'; // WPML
	$updated = wp_update_term($fi_term_id, $taxonomy, array('name' => 'Category in Finnish, updated'));
	echo "Updated FI: ".print_r($updated,true)."\n";
	
	echo "icl_translations table after updated FI translation:\n";
	$icl_translations = $wpdb->get_results("SELECT * FROM {$wpdb->prefix}icl_translations WHERE element_type = 'tax_" . $taxonomy . "'", ARRAY_A);
	foreach ($icl_translations as $row) {
		print_r($row);
		echo "\n";
	}
	echo "End of icl_translations table.\n\n";
	echo "******** END OF TEST RUN ********\n";

A revised code for the second part of the test case (line 47 forwards):

// Updating the English category
$_POST['icl_tax_' . $taxonomy . '_language'] = 'en'; // WPML
$updated = wp_update_term($en_term_id, $taxonomy, array('name' => 'Category in English, updated'));
echo "Updated EN: ".print_r($updated,true)."\n";

wpml_update_translatable_content('tax_' . $taxonomy, $updated['term_taxonomy_id'], 'en' );

echo "icl_translations table after updated EN translation:\n";
$icl_translations = $wpdb->get_results("SELECT * FROM {$wpdb->prefix}icl_translations WHERE element_type = 'tax_" . $taxonomy . "'", ARRAY_A);
foreach ($icl_translations as $row) {
    print_r($row);
    echo "\n";
}
echo "End of icl_translations table.\n\n";

// Updating the Finnish category
$_POST['icl_tax_' . $taxonomy . '_language'] = 'fi'; // WPML
$updated = wp_update_term($fi_term_id, $taxonomy, array('name' => 'Category in Finnish, updated'));
echo "Updated FI: ".print_r($updated,true)."\n";

wpml_update_translatable_content('tax_' . $taxonomy, $updated['term_taxonomy_id'], 'fi' );

echo "icl_translations table after updated FI translation:\n";
$icl_translations = $wpdb->get_results("SELECT * FROM {$wpdb->prefix}icl_translations WHERE element_type = 'tax_" . $taxonomy . "'", ARRAY_A);
foreach ($icl_translations as $row) {
    print_r($row);
    echo "\n";
}
echo "End of icl_translations table.\n\n";
echo "******** END OF TEST RUN ********\n";