Theologically speaking, "personal" refers more to the idea that God is in some sense a person, not a mindless, pantheistic life force. Relationality of some sort is probably entailed there, but interventionism certainly doesn't need to be.
Hi there Silmarien,
Firstly let me say I have enjoyed your posts immensely it is wonderful to see one who can take the complex and make it simply understood, and you are one that can do it in few words, which is indeed a gift.
It is true that theologically speaking you could interpret a personal god as one who is a person.
In Christianity however when one talks of a personal god they almost always mean a relationship, indeed if asked what makes their faith the one to be in they will often tell you it's because they are the only ones in a relationship with their God.
There are many scriptures that portray that relationship as a very close interactive one with plenty of promises.
matthew 28:20
19Therefore go and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit, 20and teaching them to obey all that I have commanded you. And surely I am with you always, to the very end of the age.”
John 14:13
12Truly, truly, I tell you, whoever believes in Me will also do the works that I am doing. He will do even greater things than these, because I am going to the Father. 13And I will do whatever you ask in My name, so that the Father may be glorified in the Son. 14If you ask Me anything in My name, I will do it.…
Matthew 18:19
Again, I tell you truly that if two of you on the earth agree about anything you ask for, it will be done for you by My Father in heaven.
James 5:15
14Is any one of you sick? He should call the elders of the church to pray over him and anoint him with oil in the name of the Lord. 15And the prayer offered in faith will restore the one who is sick. The Lord will raise him up. If he has sinned, he will be forgiven. 16Therefore confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous man has great power to prevail.…
John 14:20
19In a little while, the world will see Me no more, but you will see Me. Because I live, you also will live. 20On that day you will know that I am in My Father, and you are in Me, and I am in you. 21Whoever has My commandments and keeps them is the one who loves Me. The one who loves Me will be loved by My Father, and I will love him and reveal Myself to him.”…
I think it's reasonable, given we are on a Christian forum to interpret 'personal' as in a relationship that carries promises of intervention.