Could vs. Would
Although both ‘Could’ and ‘Would’ are Auxiliary Verbs in English Grammar and serve to modify the mood of a verb, they often confuse the learners to where and how to use them. To cope with such issue and to get an explicit idea about these Model Verbs, the underlying illustration would be of good help. First of all, we would take ‘Could’ into a discussion. Could is basically a ‘second form of can’ and is used to indicate a capability in the past e.g. ‘I could run faster in my childhood’ or ‘I could catch the thief when I saw him at first’. Hence, it replaces ‘Can’ for the past sentence; however, not only as past, it can be used in place of ‘can’ in the Present Tense to give the phrase a conditional tone such as ‘She could not allow her son to go out in the dark’. Thirdly, ‘Could’ also works to make a request more polite. For example, ‘could you let me know what your intentions are’? On the other hand, ‘Would’ is also a Model Verb and has a differential job. Firstly, it is used to indicate future in the past e.g. ‘She would try to work hard following the example of her brother’. Secondly, ‘Would’ works as the conditional mood of ‘will’ in the conditional sentences such as ‘I would get you a car if you followed my advice’. In a subjunctive case would is utilized to indicate an unreal condition e.g. ‘I would work more efficiently if I were you’. Thirdly, ‘Would’ is used for polite requests but with a questioning tone unlike ‘could’ e.g. ‘Would you like to let me know what had happened’? Moreover, ‘would’ is also used for Future Tense when there is a probability but not complete certainty e.g. ‘He would help you’ [there is a possibility that the third person will help.

Key Differences
Would is considered as the past form of ‘Will’ to indicate future in the past; ‘Could’ is the past form of ‘Can’ to indicate capability in the past.
'Could' can be used for polite requests; Would can be employed to raise a polite question.
Would can be adopted to indicate unreal thing; Could is not used for unreal things.
Could is used for possibility, while Would is used for less probability.
Could is used to suggest; Would is used in conditional sentences.
Comparison Chart
Usage
‘Could’ is the past form of ‘Can’ to indicate capability in the past
Considered as the past form of ‘Will’ to indicate the future in the past
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Language
Suggestion
Conditional sentences
Extra Uses
Polite requests
Polite questions
Adoption
Can be adapted to indicate an unreal thing
Cannot be used for unreal things

Janet White
Feb 03, 2016
Could and Would Definitions
Could
Inflection of can
Would
Past tense of will; usually followed by a bare infinitive.
Could
Used as a past subjunctive (contrary to fact).
I think he could do it if he really wanted to.
I wish I could fly!
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Would
Used to form the "anterior future", or "future in the past", indicating a futurity relative to a past time.
On my first day at University, I met the woman who would become my wife.
Could
Used to politely ask for permission to do something.
Could I borrow your coat?
Would
Used to; was or were habitually accustomed to; indicating an action in the past that happened repeatedly or commonly.
When we were younger, we would cycle out to the beach most summer Sundays.
Could
Used to politely ask for someone else to do something.
Could you proofread this email?
Would
Was or were determined to; indicating someone's insistence upon doing something.
I asked her to stay in with me, but she would go out.
Could
Used to show the possibility that something might happen.
We could rearrange the time if you like.
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Would
Could naturally have been expected to (given the tendencies of someone's character etc.).
He denied it, but then he would, wouldn't he?
Could
Used to suggest something.
You could try adding more salt to the soup.
Would
(archaic) Wanted to.
Could
Past participle of can
Would
(archaic) Used with ellipsis of the infinitive verb, or postponement to a relative clause, in various senses.
Could
Something that could happen, or could be the case, under different circumstances; a potentiality.
Would
(obsolete) Wished, desired (something).
Could
Was, should be, or would be, able, capable, or susceptible. Used as an auxiliary, in the past tense or in the conditional present.
Would
A modal verb, the subjunctive of will; usually followed by a bare infinitive.
Would
Used as the auxiliary of the simple conditional modality, indicating a state or action that is conditional on another.
If I won the lottery, I would give half the money to charity.
Would
Without explicit condition, or with loose or vague implied condition, indicating a hypothetical or imagined state or action.
I would love to come and visit.
Look at that yummy cake! I would eat that all up!
Would
Suggesting conditionality or potentiality in order to express a sense of politeness, tentativeness, indirectness, hesitancy, uncertainty, etc.
I would ask you all to sit down.
I would imagine that they have already left.
Would
Used to express what the speaker would do in another person's situation, as a means of giving a suggestion or recommendation.
It's disgraceful the way that they've treated you. I would write and complain.
Would
Used to express the speaker's belief or assumption.
He's very security-conscious, so he would have remembered to lock the door.
They would be arriving in London round about now.
Would
Used interrogatively to express a polite request; are (you) willing to …?
Would you pass the salt, please?
Would
Might wish (+ verb in past subjunctive); often used in the first person (with or without that) in the sense of "if only".
Would
Might desire; wish (something).
Would
Something that would happen, or would be the case, under different circumstances; a potentiality.
Would
Commonly used as an auxiliary verb, either in the past tense or in the conditional or optative present. See 2d & 3d Will.
Right as our Lord hath would.
Would
See 2d Weld.
Definition of Would
Would is a Model Auxiliary Verb works to modify the mood of the main verb in the sentence. It is usually used in conditional sentences as it depends on some conditions. Would also be used for sentences in which something is being said about the future but in the context of the past. This model verb can also be employed to raise polite questions as well.
Definition of Could
Could is a Model Auxiliary Verb and normally used in place of ‘Can’ for Past Tenses to highlight past capability. Apart from showing capability in the past, ‘Could’ is also used frequently to make polite requests. It is used for possibility e.g. ‘they could have done this job more effectively’.