Could someone write just your card number to a blank card? Yes. But would that let them masquerade as you and charge up your account by swiping that card at point of sale machines in brick and mortar stores? No. Mainly because, when a transaction is sent from a point of sale machine to a card processor for validation, they require data besides the card number (just like you mention for online transactions). Those other required data elements are also written to the mag stripe, in addition to the account number, on a valid card.
Credit card mag stripes contain three tracks - the first two are essentially standard, and describe your account (including account number, expiration date, your full name, country code, etc). Those two tracks are what's used to actually process a transaction when the card is swiped, and essentially replicate the info you're used to typing in when using your card online.
The third track is largely unused, and when it is used, the info stored there varies bank to bank - sometimes including things like PIN numbers, or ID numbers associated with rewards programs, or your max line of credit, or other info. It's essentially unimportant in the scenario of validating a transaction at a point of sale machine, though.