The same G-d

Is G-d the same in the Old Testament as the New Testament. It is amazing how some people will say he is not, even though Yeshua said pretty much the same thing as G-d did. He does tell us we are the vines and His Father Prunes the vines and branches and puts the branches which are not baring fruit into the fire. That to me sounds like the Same G-d as the Old Testament. To be removed from the branch is not seen as a good thing, but to be pruned would be good, pruning encourages what ever being grown to grow more and produce more fruit.
We are coming up to the fall festivals, I didn’t realize this until recently but my graduation commencement is on one of the festivals. The festivals are appointed time from G-d which most of my Christian Brother and Sisters have very little knowledge and don’t practice even though their savior did. This times were not did away with, they are going to be until the end of time.
G-d loves us but as a father does with his children as long as we listen he will guide us. Like a map guides a long distance moving companies to find the best route to the end point. We need the Word of G-d but at the same time we need to understand the mind set and what his disciples would have believed and done. We can not take the bible and put it into modern day terms because there is not much which actually fits.