Answers for your questions.

First = 사은품. Second = 증정품.

Let's say you go to a shop to buy a pencil. In that shop, workers give customers a eraser as a 증정품. You can get 증정품 for free if you buy a pencil or not. 

For customers buying a pencil, the shop gives a note as a 사은품. You can get 사은품 if you meet a certain condition which is buying a pencil in this case.

That condition can be anything. Buying something or Buying over some amount of money.

증정품 > 사은품 으로 ..  사은품은 물건을 사면 주는 선물? 같은거..

증정품은 사은품과 같이 물건을 사면 주는 선물도 있지만, 물건을 안사도 홍보등을 위해 그냥 주는 선물일수도 있으므로,

증정품이 더 큰 의미라고 보면 됩니다.

Hello, Briana.

If you break words down, it will help you out to understand the difference of similar words

Even though I am a native Korean, I normally use this method when I am confused with them.

So let's break it down.

1. 사은품 : 사은(an expression of gratitude) + 품(=an Item)

You can use '사은' as a verb which is '사은하다.'. It means 'express gratitude'

(*Not many people use this verb nowadays though.)

Basically '사은품' is an item that somebody expresses gratitude through giving it.

In the commercial field when you purchased something they thanked you. So they gave you another gift.

That's '사은품'.

2. 증정품 : 증정(=giving something away) + 품(=an Item)

You can also use '증정' as a verb which is '증정하다.'. It means 'give away.'.

I've seen a number of people using 'giveaway' on the internet to promote their website or goods.

I guess that's equivalent to '증정품'.

Basically it's similar to '사은품', but it's a bigger version of it, because whether you buy something or not it can be given.