We often hear that Higgs boson is a scalar boson, and that Higgs field is a scalar field. I was always thinking that this means "4-scalar". In other words, it is space-time invariant, .i.e. it's properties are not changing if move relative to it. Unlike photon which changes it's frequency, polarization and other properties, if we look at it from moving frame, Higgs is always the same.
Is above correct? If not then what is correct and what is not?