The difference between "いる/います" and "ある/あります"

Question: I keep messing up "いる/います" and "ある/あります". Can someone help like the main meaning or example sentences?

"いる" is used to describe the existence of something.

"います" is a polite variation of "いる".

"ある" is used to describe the existence of something, same as "いる".

"あります" is a polite variation of "ある".

The meanings of these words are similar, but not identical.

Major difference is that:
"いる/います" is used to describe the existence of something living, which can move by itself.
If something is not a living creature, use "ある/あります" instead.

Example as follows:
    There is a dog. 　そこに犬がいます。
    There is a book. そこに本があります。

However, there are some exceptions. Such as:
    There is a taxi. 　そこにタクシーがいます。

A taxi is not a living creature, but in this case we Japanese use "いる/います".
I think that, a taxi is not living itself, but it can move like an animal can. So Japanese people consider it as living.
It is same as a train, ship, airplane or anything that can move.

And one more exception.

If someone lost something and he began to search for it. For example, when I lost my house key and began to search my house.

In this situation, when I found it, I can say "あった、あった" or "いた、いた" to mean "I found it".

A house key is not living, so ordinary usage of existence is "ある/あります". ("あった" is a past tense of "ある")

But in this case we can use "いた" (past tense of "いる") too.

I think that in this case we feel that something had gone away against our will, as if it were an animal which could move by itself. So we use "いた" when we find it.

FYI

"あった、あった" or "いた、いた" both are repeating expression of a simple word.

If I say just "あった", it means just "I found it".

If I say "あった、あった", it means "Oh, I found it!".

Repeating expression indicates a little exclamation.