It is common in BrE to use 'contact number' where AmE would use 'telephone number'. Does the 'contact' in 'contact number' refer to the act of making contact, or is there a more technical origin, as in the number of a specific electrical contact in the telephone system?
Contact number specifically refers to a telephone number which someone can use at a specific time.
Whereas asking for, "Telephone Number," may encourage someone to put their home (landline) telephone number, if this is for a business to contact them, the person is possibly going to be at work themselves when the business attempts to contact them. Therefore a more suitable number would be a mobile or office number.
A contact number can mean "phone number", especially on official forms. "Contact" here refers to the act of making contact. It does not have a (widely-used) specialist electrical meaning.
That said, it's worth adding that I use contact number, and hear it being used, when I am giving someone a phone number that is not my usual phone number but one I may be reached on - "contacted" - due to some temporary circumstance when my usual phone number may not work (e.g. on holiday, a business trip or staying with someone).
From Collins Dictionary:
contact number (in British)
a person's telephone number
- Do you have a contact number for James?
verb (used with object)
- to put or bring into contact.
to communicate with:
We'll contact you by mail or telephone.
Quite simply the "contact" is to do with the verb "to contact", i.e. "to communicate with".
A "contact number" is a number you can use to communicate with someone, or in other words a number they ca be contacted on.