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 join you at that location?
Are they able to gain access to the business centers?
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.
He can make the reservations for us.
Country clubs are able to exclude people based on income or credit rating.
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.
Larry has been able to lose weight and eat pastries every day.
Larry has been able to find a new manager familiar with motel operations.
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.
He was able to correct his time management issues last month.
Jenny was able to provide limousine rentals to the diplomats at the conference.
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
The hotel was able to provide special services to customers with special needs.
I could enjoy casual dining as well as fine dining after the course.