Understanding Relationship Terms

Barbara wanted to know about relationship terms.

Can you tell me which of the following ‘removed’ are the equivalent of  3^rd great grandfather (e.g.) That is, is a 3^rd great grandfather the same as Third removed?

Are the two terms used for different reasons or can either be used.

The following is from other notes but I’m still none the wiser. "When cousins descend from common ancestors by a different number of generations they are called "removed."

Once removed means there is a difference of one generation. Your mother's first cousin would be your first cousin, once removed. She is one generation younger than your grandparents and you are two generations younger than your grandparents.

Twice removed means that there is a two-generation difference. Your grandmother's first cousin would be your first cousin, twice removed because you are separated by two generations."

Barbara, 

The short answer to your question is "No". The terms are quite different.

Since you have the correct definition of the terms "once removed" and "twice removed" but it's puzzling you, let me try to explain it a different way. You use the term "removed" when you are comparing two individuals to a common (shared) ancestor. So you need 3 people in the mix! "Removed" means the two individuals are a certain number of generations apart. 

Let's say you have a relative named Sally. Sally's father and your father are brothers. That makes you and Sally first cousins. 

Now let's say you have a child named Roger. Roger is also Sally's first cousin BUT he is one generation removed from her! That makes Sally and Roger first cousins once removed.

Your 3rd great-grandfather refers to a relationship between 2 people -you and your 3rd. great grandfather.