The simple answer is: they didn't.
If they weren't literate (do you have any evidence they were?), then for the census they would have given their details verbally to somebody else to write down (e.g. census enumerator, or a neighbour) who wrote down what they thought they heard. And if the family concerned were illiterate, they wouldn't spot a mismatch. The enumerator then copied the details into his enumerator's book -- so another opportunity for differences to creep in.
The birth certificate was filled in by the registrar not by the family, based on verbal details again. And, if you got a certificate from the GRO, what you've got is a copy of a copy of the original. The registrar filled it in; a hand-written copy was made to send to the GRO who (a century or more later) have copied it for you -- if you're lucky, you'll have an image of the hand-written copy -- but I've received typed transcriptions made by the GRO before now when their copy couldn't be copied. Lots more opportunities for spelling to be altered.
Also of note: standardised spelling is a very recent concept, so it shouldn't be called mis-spelling but variant spelling.