Change (replace) tags to tags

As @Sally CJ mentioned, you should set a result of str_replace() to a variable.

For a content you chose a right filter – the_content, for tinymce editor you need to use the_editor filter.

As they a similar, you can use one function for both filters.
In my example I use only one str_replace for opening and closing tags.
Basically, it will be enough, unless you have ‘b>’ text in your content to.

function change_b_to_strong($content){
    $content = str_replace('b>', 'strong>', $content);
    return $content;
}

add_filter( 'the_content', 'change_b_to_strong' );
add_filter( 'the_editor', 'change_b_to_strong' );

Update

If you output content using get_the_content for example, this filter will never fire.
You can apply the_content filter to your text also.

$content = get_the_content();
$content = apply_filters('the_content', $content);