difference between section, part, and piece

part 

some

1 [uncountable] part of something
                          some but not all of a thing

• We spent part of the time in the museum. 
• Part of the building was destroyed in the fire.

piece

2 [countable] a section, piece, or feature of something

• The early part of her life was spent in Paris. 
• The novel is good in parts. 
• We've done the difficult part of the job.

member

3 [uncountable] a member of something; a person or thing that, together with others,   
                           makes up a single unit

• You need to be able to work as part of a team.

region/area

4[countable] an area or a region of the world, a country, a town, etc.  

• the northern part of the country .
• a plant that grows in many parts of the world 

of body/plant

5 [countable] a separate piece or area of a human or animal body or of a plant 

• the parts of the body

section  

part/piece

1[countable] any of the parts into which something is divided 

• That section of the road is still closed. 
• The library has a large biology section.

of document/book

2[countable] a separate part of a document, book, etc.

• These issues will be discussed more fully in the next section. 
• the sports section of the newspaper

group of people

3[countable] a separate group within a larger group of people

• an issue that will affect large sections of the population 
• the brass section of an orchestra

district

4[countable] a district of a town, city, or county

• the Dorchester section of Boston

of organization

5[countable] a department in an organization, institution, etc. 

• He's the director of the finance section.
•  the section of the company dealing with customer services

piece

 

separate amount

1[countable] piece (of something) 

(used especially with of and uncountable nouns) an amount of something that has been cut or separated from the rest of it; a standard amount of something

• a piece of string/wood.
• She wrote something on a small piece of paper.

part

2[countable, usually plural] one of the bits or parts that something breaks into

• There were tiny pieces of glass all over the road.

single item

3[countable] (used especially with of and uncountable nouns) a single item of a particular type, especially one that forms part of a set

• a piece of clothing/furniture/luggage.
•  a piece of equipment/machinery

4[countable] piece of something  

used with many uncountable nouns to describe a single example or an amount of something

• a piece of advice/information/news.
• an interesting piece of research

news article

5[countable] an article in a newspaper or magazine, or a broadcast on television or radio

• Did you see her piece about the Internet in the paper today?

coin

6[countable] a coin of the value mentioned 

• a five-cent piece