There is a difference.
Liberals want big government where it makes sense: addressing societal problems and needs in sectors where the private market is ineffective or produces unacceptable outcomes.
Conservatives want big government where it doesn't make sense: imposing the same set of morals on everybody, regulating what goes into your body, etc.
Federalism is not a big government/small government. It's simply a method of giving different powers to different levels of government.
It's more costly to maintain than a unitary government, but it also allows for increased democratic participation, for localities to customize their government to fit their needs, and for "laboratories of democracy" - experimentation with policy on a small scale that can then be attempted on a larger scale if it is successful.
Despite the benefits of giving power to local governments, the national government must be empowered to protect states and municipalities from violating fundamental rights, to resolve disputes and simplify interactions between states, and to undertake tasks that are necessary for the nation as a whole but that individual states don't have the ability or incentive to undertake.
I'd have to put marriage in the national group, myself, since having marriages that become valid or invalid depending on what state you are in is bonkers.
On a tangent, I would argue that liberals want to forcibly impose their morality on others as well.
