DNA consists of two strands bonded together through the nucleobases C G A T the order of which specifies the coding information. C is always paired with G, A with T.
So if you know the coding sequence of one strand, you know that the other strand will be the alternative - ie CGAT on one, GCTA on the opposite.
So the two sources you quote are just reporting results for opposite strands.
When a SNP involves a change from C to T as in your example - ie bases which don't pair with each other - it doesn't matter which strand the result is reported from. You can always work out if you have the variant or wild-type allele.
When a SNP involves a change from G to C or from A to T you need to know which strand the result is coming from to know which version you have.
23andme always reports results for the forward or plus strand, but other sources might report from either strand (the opposite strand is usually designated - or reverse).
You can always check this
here by just typing in the rs number of the SNP you are interested in. You will get a lot of information, including which allele is wild type, which is variant (including the orientation) as well as frequency in the population, references to research, etc.