Two different things. The $10,000 cap refers to the itemized deduction for state and local taxes (income, property and sales taxes), known as SALT.
The standard deduction for Married Filing Separately (MFS) is $12,000 each (half of the $24,000 for married filing jointly-MFJ).
The $10K SALT deduction is just one piece of total itemized deductions (you can add charity and medical to that).
But here's the kicker: if you file MFS and one of you itemizes deductions, the other must also itemize. She cannot use the $12K standard deduction, if you itemize. So, if you're trying to beat the system by filing separately, it won't work.
