If the http:// or https:// prefix isn't included and the link is surrounded by [url]...[/url], the rendered link is incorrect.

CORRECT (no BBcode):

www.example.com

INCORRECT (includes [url] BBcode):

[url]www.example.com[/url]

For example, posting the latter markup on phpbb.com produces this target:

https://www.phpbb.com/community/www.example.com

The correct target is generated if the https prefix is included.