"Unregistered" means the SIM is not registered on any person, so you can still register it on your name and so be the official owner, which is a legal requirement in many countries. Failure to do so may result in deactivation of your SIM.
"Active" just means the SIM is working. There are countries, where you first need to register in order the SIM to be activated, but my 3 UK SIM is definitely working without being registered.
Afaik 3 UK don't accept foreign credit cards for recharges through their website. However I was able to top up credit with tuyo (USA) and T-Mobile UK with my German AmEx allthough neither my German Visa nor Mastercard were accepted by both - so if you have an AmEx just try it. Otherwise there's still
TopUpForLess, who sell recharge codes for most British providers below nominal value(!) and they accept PayPal besides all major credit cards. So these guys are perfect for topping up from abroad, which I've done successfully several times. Just note, that they want new customers to request acceptance as such in advance by eMail.