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 click on this icon?
Will I be allowed to reconfigure the seat of our network?
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 run a script to control all of our programs.
Jane is able to get an include on every important webpage.
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 the rural American is going to be able to get high speed internet in 2030.
John has been able to obtain an interlaced system.
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.
Jenny was able to install her own upgrade.
I was able to set up a chat session with the CEO last night.
'Could' and 'was / were able to' are also used to express a general ability in the past in the positive and negative forms.
I was able to lurk on that forum for months.
He could install the SCSI cable whenever the system rebooted.