No, for taxes, married filing separately is a different category than single. Married filing separately results in a higher tax bill than married filing jointly for most couples.
There are places in the tax code where Single != Married Filing Separately.
One pertinent example is that Washington State's capital gains tax applies after $270k per single person, per married couple filing jointly OR split in half for married filing separately. Which could be a theoretical $18.9k/year difference in taxes.