What's the difference an idiom and a saying?​

1. We decided to postpone _the_ party for _a_ week.
2. It was _an_ ugly house with too many passages and _a_ glass porch.
3. Peter is _a_ friend of mine.
4. They tried to break _the_ lock with _a_ sledgehammer.
5. __ kings live in __ palaces.
6. An educated man is not happy without __ books.
7. _The_ palm trees along the beach are very tall.
8. Sorry if _the_ truth hurts.
9. From the window she had _an_ enthralling view of the city.
10. I won’t forget you in _a_ hurry.
11. He recognized her at __ first sight.
12. When we last played __ golf you were terrible.
13. She works as _a_ chemist.
14. _The_ sun was getting warmer.
15. We went to _the_ cinema last night.
16. I like ___ ice-cream.
17. He repeated it over and over again until he knew it by heart.
18. Here is _the_ book I told you about.
19. In front of _the_ station there was _an_ elm tree.
20. It was very hot for _the_ time of year.

1. to open
2. ing
3. ing
4. look at 
5. to announce
6. quitting
7. selling it
8. describing 

1. Компания была известна своими достижениями в снижениях затрат и увеличения производства.
2. Исследования опубликованные год назад показывают что продажи здоровой товаров увеличились на 20%
3. Идея заказать новые товары может быть очень привлекательна для компании.
4. Закончив письмо Адвокат вышел из комнаты. 
5.Маркетинговый исследователь делает подробный план для его исследований проблем включая какой источник данных он будет использовать.