Speaking about Abilities
Can - Be Allowed to
'Can' is used to ask for and give permission. In the simplest sense, we use 'can' to request something. However, at other times 'can' expresses permission to do something specific. 'May' is also used in a more formal sense. In American English, 'May I ...' is considered the correct formal form to ask for permission.
'To be allowed to' can also be used to ask for and give permission. This form is more formal and is commonly used for rules and regulations.
Examples of Asking Permission
Can I borrow your car?
Is accounting able to file the invoicing reports early?
Can - To Be Able To
'Can' is commonly used to express the ability to do something. This usage is similar to the form 'to be able to do something'. Both these forms are acceptable, although 'can' is more commonly used.
Jim can explain what the accrued liability is.
John was able to talk the bond holder into the agreement.
To Be Able To - Future and Perfect Forms
There is no future or perfect form of 'can'. Use 'to be able to' in all future and perfect tenses.
Susan has been able to replace her lost debit card.
The issuing bank will not be able to activate the card until tomorrow.
Special Case of the Past Positive
Use 'was / were able to' when speaking about a specific event in the past in the positive form. Both 'can' and 'to be able to' are used in the past negative to speak about specific events.
Stanley was able to find out his credit rating.
Were you able to do the invoicing for the credit department?
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
He was able to rely on savings banks in the past.
The mortgage amortization could have been discounted during its first five years.