Did vs. Done
First of all, Did is used only for Past Indefinite/Simple Tense to indicate something which is occurred recently. Did, the auxiliary verb, is considered to be the second form of Do and it is used to refer to anything thing which is over and has become the part of past, recent past. According to the grammatical rules for making sentences, Did can never be used for any other Tense rather than the Past Indefinite/Simple e.g. 'I did my work yesterday', 'Did you do what you were asked to?' As far the Interrogative Sentences are concerned, 'Did' is always used to ask 'Affirmations' or Confirmation for something, e.g. 'Did she perform nicely.' One thing must be kept in mind that 'Did' is followed by the First Form of Verb if there is only one Subject in the sentence. e.g. 'Did you watch the match last night'? However, if you are to use the Subject more than once in the single sentence, you are bound to use the second form of verb for the second subject as well. e.g. 'I did watch the movie and I liked it very much'. On the other hand, Done, the third form of 'Do', is named as Past Participle in grammatical terms. Unlike Did, the third form of Do never comes alone but it needs another helping verb to make a sensible sentence. In contrast to Did, Done can be seen in sentences of any Tense and will always be used after helping verb e.g. Is, Am, Are, Be, Has, Have, Had. This construction is used to describe about something which is completed either in the Present, Past or even Future as this word is Free from such restrictions as we have for Did. In Active Voice, 'Done' is always used to say that something is completed. e.g. 'I have done my work', 'Students had done their home work before leaving for school.'

Key Differences
Did' is the second form of 'Do' while 'Done' is the third form of 'Do'.
'Did' is always used for Past Indefinite/Simple Tense, while 'Done' is pliant and can be used in all Tenses.
'Done' can be used in both Voices - Active, Passive -, while 'Did' cannot be used in Passive sentences.
'Did' indicates towards something which is over, while 'Done' says that something is completed.
Comparison Chart
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‘Did’ is the second form of ‘Do’.
‘Done’ is the third form of ‘Do’.
Tense
‘Did’ is always used for Past Indefinite/Simple Tense
‘Done’ is pliant and can be used in all Tenses.
Explanation
‘Did’ indicates towards something which is over
‘Done’ says that something is completed.
Structure
‘Did’ cannot be used in Passive sentences.
‘Done’ can be used in both Voices – Active, Passive
Did and Done Definitions
Done
Past participle of do1.
Done
Having been carried out or accomplished; finished
A done deed.
Done
Socially acceptable
Spitting on the street is just not done in polite society.
Done
(Informal) Totally worn out; exhausted.
Done
Having completed or finished an activity.
He pushed his empty plate away, sighed and pronounced "I am done."
They were done playing and were picking up the toys when he arrived.
Done
(of an activity or task) Completed or finished.
I'll text you when the movie's done.
Done
(of food) Ready, fully cooked.
As soon as the potatoes are done we can sit down and eat.
Done
Being exhausted or fully spent.
When the water is done we will only be able to go on for a few days.
Done
Without hope or prospect of completion or success.
He is done, after three falls there is no chance he will be able to finish.
Done
Fashionable, socially acceptable, tasteful.
I can't believe he just walked up and spoke to her like that, those kind of things just aren't done!
What is the done thing these days? I can't keep up!
Done
Inflection of do
I have done my work.
Done
Used in forming the perfective aspect; have.
I woke up and found out she done left.
Done
(slang) methadone
On the done
Done
It is done or agreed; let it be a match or bargain; - used elliptically.
Done
Given; executed; issued; made public; - used chiefly in the clause giving the date of a proclamation or public act.
Done
Having finished or arrived at completion;
Certain to make history before he's done
It's a done deed
After the treatment, the patient is through except for follow-up
Almost through with his studies
Done
Cooked until ready to serve
Definition of Did
‘Did’ is the second form of Do. It is always used under Past Indefinite/Simple Tense. We employ ‘Did’ whenever to say that something is over in recent past. Did is considered as a helping/auxiliary verb and can also be used as an additional Word to form Interrogative sentence to seek Confirmation. e.g ‘Did you complete your assignment?’ The helping verb ‘Did’ can never be used in other Tenses like Present Indefinite, Perfect, Continuous and Future. It is only used in the Past Indefinite/Simple Tense.
Definition of Done
‘Done’ is the third form/past participle of ‘Do’. As a third form, it is relatively flexible and can be utilized under any Tense to indicate something which is completed. It can be used to say that some task is accomplished and it is always comes after the helping verbs such as ‘Is, Are, Am, Has, Have, Had, Be’. e.g. ‘Her work is done,’ ‘We have done our work’ etc.
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