つつ

つつ is a particle that attaches to the ます stem of verbs.
It means While or Despite.


Unlike ながら, it may not attach to adjectives or directly to nouns (Noun + でありつつ is ok).
ながら is

While

While
Verb ます Stem + つつ
Noun + でありつつ
Adjectives ✖

The most basic meaning of つつ is “while”.
Meaning wise, its the same as ながら, but generally only written instead of spoken.

*Personal note:
To me, つつ feels more equal than ながら, which has a main and sub action.

Examples

• 掃除しつつ、鍵を探す – Search for the key while cleaning.
• 作成しつつ調べる – Look it up while making it.
• お茶を飲みつつ本をよむ – Read a book while drinking tea. 
  
  

Despite

Despite
Verb ます Stem + つつ
Noun + でありつつ
Adjectives ✖

つつ can also mean “While” in a despite sense.
Sentences like: “While knowing that X is bad…did it anyway”
This meaning may become つつも
Almost the same as ながらも

Examples

• 犯罪だと知りつつ、車を盗んだ – While knowing it was a crime, stole a car.
• 謝りつつも、行動を続けた – Continued despite apologizing. 
• 敬語を使いつつも、無礼な態度を取った – Despite using Keigo, had a rude attitude. 
• 公開しつつも、やめなかった – Despite regretting it, did not stop. 

つつある

In progress
State + つつある

つつ can be combine with ある to indicate a currently continuing state. (Literally: Existing while”)
つつある can be used as てある or ている. (Animate/inanimate doesn’t matter”.)
It differs from ている/ある in that it means “While ~ing” instead of just “~ing”. (No real difference).

つつある is also mostly written rather than spoken.

Examples

• 雨は降りつつある – Rain was continuing to fall. (Was being fall)
• 習慣は変わりつつある – The customs are changing (In the process of). 
• 消えつつある – Disappearing. 

VS. ながら

ながら is used more in conversation and has broader usages.
つつ is more formal/written, and cannot attach to adjectives or nouns (でありつつ is ok).
Aside from that they are the same.
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