The most common use of the word, giving birth to a child, is perhaps one of the more miraculous and inspiring events ever to be witnessed.
But it can be used similarly in giving birth to an idea. More generally it could be said that it is the coming into existence of something, animate or inanimate.
It can be used to state lineage or descent, i.e. he was Italian by birth, or he was a Duke by birth, but a politician by trade.
You could use birth pain in other expressions like trying to get a club or team together, those initial stages where everything goes wrong.
And that old favourite, wanted by every man and his dog, what is your date of birth?
On the other hand, a berth is a place where a ship or boat ties up after a long or short voyage.
It’s also a bed on a ship, not necessarily in a stateroom, but could be in one of those shared cabins below the waterline that do not cost a lot, and only a place to sleep, or for some, to recuperate. It doesn’t necessarily have to be on a ship, it could be on a train.
It could be the distance between two ships or the shore.
You could also use it to describe your job or position in the company.
Then, you could say you gave the enemy’s camp a wide berth, or just a group of people we don’t want to pass in the street.