A christian ask about those verses: 8:12 Remember thy Lord inspired the angels (with the message): “I am with you: give firmness to the Believers: I will instil terror into the hearts of the Unbelievers: smite ye above their necks and smite all their finger-tips off them.” And this one But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, an seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practise regular charity, then open the way for them: for Allah is Oft-forgiving, Most Merciful 9:5
The first verse talks about the battle of Badr where 300 plus Muslim soldiers faced over 1,000 pagan soldiers and managed to win the battle. So, it was about a battle.
The second verse is about the truce between the Muslims who conquered Makkah and the pagans whom been given 4 months to evacuate the area and never to come back again. This is because they broke the treaty they had with Our Prophet peace and praise of Allah be upon him. He didn’t order them to be executed on the spot but rather to be given 4 months to think it over and either leave or stay as Muslims.