Is could always a past tense?

No, and treating it as one causes trouble. Could you help? is a present request, and it could rain is present possibility. Only in the general-ability sense is it genuinely the past of can, which is why context rather than form tells you which it is.

Why is couldn’t fine for a single occasion but could isn’t?

Because a failed attempt and a lack of ability come to the same thing, so English does not bother distinguishing them. Success needs the distinction. You might be able to do something and still not have done it, which is why only the positive requires was able to.

What about could have?

It describes an unrealised past possibility: I could have taken the earlier train, meaning it was possible and I did not. That is different again from was able to, which reports something that actually happened.

Which one to useB1

Can vs could vs be able to

The short answer

Can covers present ability, could covers general past ability, and be able to fills every gap the two modals cannot reach: the future, the perfect, and any position after another modal. For a single successful effort in the past, English prefers was able to or managed to.

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At a glance

Can / could or Be able to?

Compare	Can / couldModals. Present and general past.	Be able toFills every other tense and position.
Present	can swim	am able to swim: more formal
General past ability	could swim at five	was able to swim
One successful occasion	Not used	was able to / managed to
Future	No form	will be able to
Perfect	No form	has been able to
After another modal	Not possible	might be able to

How to choose

Ask these, in order

1
Is it present ability?
Can. Be able to works but sounds formal.
She can read Arabic.
A present skill.
2
Is it a general ability in the past?
Could.
I could run much faster then.
A standing ability over a period.
3
Did it succeed on one particular occasion?
Was able to, or managed to. Could would be wrong here.
The fire spread quickly, but everyone was able to get out.
One event, one success.
NBEveryone could get out would describe an ability, not what happened.
4
Do you need a future, a perfect, or a slot after another modal?
Be able to, the modals have no forms there.
You might be able to catch the last train.
Two modals cannot stack.

Side by side

Each one, in full

Can / could

Can and could

Modals. Present and general past.

Can expresses present ability, permission and possibility, and takes a bare infinitive: I can help. Could is its past for general ability: when I was young, I could stay up all night, and also a softer present for requests and possibility.

Neither has a future, a perfect or an infinitive form, which is the structural fact that drives everything else on this page. There is no will can, no have could and no to can.

Can you hear me?

Present ability.

Could you send it again?

A polite request, not a past.

It could rain later.

Present possibility.

Be able to

Fills every other tense and position.

Be able to conjugates freely, so it covers every gap: will be able to, have been able to, might be able to, to be able to, being able to. In the present it is correct but stiffer than can, so it is worth reserving for the slots can cannot fill.

Its critical use is the single successful past effort: after two attempts I was able to open it. Could there would say you had a standing ability rather than reporting that it worked, and in the negative the distinction disappears, because couldn’t is fine for both.

I’ll be able to confirm on Monday.

Future, can has no form.

We haven’t been able to reach her.

Perfect, again, no modal form.

I couldn’t get through, so I emailed instead.

Negative, couldn’t works for a single occasion.

Mistakes to avoid

What learners actually get wrong

Yesterday I could finally fix the printer.
Yesterday I was able to fix the printer. / I managed to fix the printer.
Could describes a standing ability, not a single success. For one occasion that came off, English needs was able to or managed to, and in the negative, couldn’t would have been fine.
I will can help you tomorrow.
I’ll be able to help you tomorrow.
Two modals cannot stack, and can has no future form at all. Be able to exists precisely to fill this position.
I have could speak Italian since childhood.
I have been able to speak Italian since childhood.
There is no perfect form of can. Any perfect, infinitive or participle use of ability has to go through be able to.
Can you to swim?
Can you swim?
Modals take a bare infinitive with no to. Be able to keeps its to, which is exactly where the confusion comes from, the two constructions behave differently in the same slot.

Now use it

Modal verbs

can, must, should, have to: obligation, advice and deduction. Reading a rule and being able to apply it are different skills, and only one of them shows up when you speak.

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Questions

Asked and answered

Is could always a past tense?: No, and treating it as one causes trouble. Could you help? is a present request, and it could rain is present possibility. Only in the general-ability sense is it genuinely the past of can, which is why context rather than form tells you which it is.
Why is couldn’t fine for a single occasion but could isn’t?: Because a failed attempt and a lack of ability come to the same thing, so English does not bother distinguishing them. Success needs the distinction. You might be able to do something and still not have done it, which is why only the positive requires was able to.
What about could have?: It describes an unrealised past possibility: I could have taken the earlier train, meaning it was possible and I did not. That is different again from was able to, which reports something that actually happened.

Keep going

Must vs have toB1Must is obligation you impose on yourself; have to is obligation imposed from outside.