The essential concept of questioning is inquiry that generally ends with a question (?) mark, and the essential concept of doubting is uncertainty that generally ends with an exclamatory (!) mark.
You call something a question when you want to know about something, like, "Is there a God"? You call something a doubt when you know something but not sure whether it's correct, and you want to have clarification on it through doubt, like "I doubt that the God of Bible is the real God"!
Questioning and doubting are not mutually exclusive. For instance, while I DOUBT there’s a supreme being, my DOUBT could change, if certain fundamental QUESTIONS were definitively answered. But will those QUESTIONS ever be definitively answered? I DOUBT it! However, the ideal null hypothesis, or starting premise, should be met with the question, “Is this true”?, and doubt should be met with the exclamation, "I seriously doubt it this is true"!
Questioning is when an individual is still actively seeking answers to a conundrum. Doubting is when an individual is at a stand still or at the end of their investigative search. Not knowing which way to turn, to seek further information or clarification of the information they have already obtained.
It is two sides of the same coin. Questioning generally means you are honestly seeking answers. Doubting comes from the same source but is accompanied by apathy, you really don't care about the answer.
The answer depends on the situation. If one is faithful to a religion, he/she is probably going to have short and infrequent moments of questioning. But others may have frequent moments of doubt. The doubt usually results in questioning. However, questioning (because of doubt of everything, or, perhaps, full open-mindedness in everything) can also lead to faith. If a non-believer is questioning his/her current belief, or just questioning anything or everything, it may lead the person to believing in and being faithful to one thing, such as Christianity. At first, when being introduced to the religion, he/she will have some doubts before the faith comes. So no, they are not the same thing. One may question because of doubt, or one may question to eliminate doubt. I hope my rambling made sense...
Doubt often leads to questioning. If you doubt a premise's veracity, would you not then ask questions to determine whether that premise held true or not?
For example, when I was still Christian there were certain claims and stories I had doubts about, as they just didn't seem to make sense. As a result, I asked questions and did research to find the answers. So I don't know how that quote you were given makes a lick of sense- all questions have doubt at their core. If you didn't doubt something, why would you question in the first place? You'd have no need to.
Even the Bible says: "Dearly Loved friends , don 't always believe everything you hear just because someone says it is a message from God; test it first to see if it really is. For there are many false teachers around.(1 John 4:1) Living Bible. As you can see on ask.Com, everyone has a different point of view. " Now the Spirit speaketh expressly, that in the latter times Some shall depart from the faith, giving heed to seducing spirits, and doctrines of demons." ( 2 Timothy 4:1) KingJames Version What Jesus taught was the truth, what many teach today is not. It's up to you to find out what is the truth? What does the Bible really teach. " Not all who sound religious are really godly people. They may refer to me as Lord,' but still won't get to heaven. For the decisive question is whether they obey my Father in heaven. At the Judgement many will tell me, Lord, Lord, we told others about you and used your name to cast out demons and to do many other great miracles.' But I will reply , You have never been mine. Go Away, for your deeds are evil." ( Matthew 7:20-23). Living Bible
Questioning is trying to find an answer to something you don't fully understand. Doubting is wondering if what you already know is wrong. - As always, I'd enjoy discussing anything you'd like in whatever detail you want.