What are the really difference writing WordPress 3.x widget plugins?

I have read a lot of turorials an even the codex widget API, but can’t solve my doubts: What are the really difference writing WorPress 3.x widget plugins? if there exists.

this doubt came when trying to create plugin containing an widget I have actived WP_DEBUG and saw the notice that register_sidebar_widget() is deprecated and I should use wp_register_sidebar_widget() instead.

So I have changed and now I get:

Notice: Uninitialized string offset: 0
in
/…/wp-content/plugins/raz/index.php
on line 54

Notice: Uninitialized string offset: 0
in
/…/wp-content/plugins/raz/index.php
on line 55

Notice: Uninitialized string offset: 0
in
/…/wp-content/plugins/raz/index.php
on line 55

Here is the code:

<?php

// widget to show an iframe containing Brazilian CPTEC weather forecast
function previsao_tempo_cptec_widget_display($args) {

  // print some HTML for the widget to display here
  print $args['before_widget'];
  print $args['before_title'] . "Previsão IN TITLE do Tempo - CPTEC" . $args['after_title'];

  //  print "content of the widget";
  print '<center><!-- Widget Previs&atilde;o de Tempo CPTEC/INPE --><iframe allowtransparency="true" marginwidth="0" marginheight="0" hspace="0" vspace="0" frameborder="0" scrolling="no" src="http://www.cptec.inpe.br/widget/widget.php?p=4599&w=h&c=909090&f=ffffff" height="200px" width="215px"></iframe><noscript>Previs&atilde;o de <a href="http://www.cptec.inpe.br/cidades/tempo/4599">Santa Maria/RS</a> oferecido por <a href="http://www.cptec.inpe.br">CPTEC/INPE</a></noscript><!-- Widget Previs&atilde;o de Tempo CPTEC/INPE --></center>';
  print $args['after_widget'];   

}

// Activate the sidebar
wp_register_sidebar_widget(    
    'TempoCPTEC_1',  
    'Previsão de Tempo - CPTEC',     
    'previsao_tempo_cptec_widget_display',  
    array(
        'description' => "Este  widget mostra a previsão de Tempo  pelo CPTEC - INPE/BR"      
    ),
    array(
    'before_widget' => '<li>',
    'after_widget'  => '</li>',
    'before_title'  => '<h2 class="widgettitle">',
    'after_title'   => '</h2>'
    )
);


// Loads the widget
add_action('widgets_init','previsao_tempo_cptec_widget_display');
?>

Other doubt, why this widget is always displayed in the top of my website and in the sidebar
widgets also?

Thanks for any incoming handy answer.