Yes, each valence lattice vacancy (hole) is always a cation, since holes are always part of postive-charged atoms. Electrons are different, since they can be part of a neutral, un-ionized atom.
In p-type semiconductor, because of thermal vibration, each neutral acceptor dopant atom (say boron) will grab an electron from a neutral silicon neighbor. This creates a pair of opposite charges: a negative boron ion and a positive silicon ion. The boron now has excess negative charge (more electrons than protons,) while the silicon has excess positive charge (more protons than electrons.) But then the magic happens: that positive silicon ion can grab an electron from a silicon neighbor, ionizing the neighbor while becoming neutral itself. At the same time the negative boron ion remains trapped. Thermal vibrations knock the mobile charges around, so the opposite charges soon are widely separated. The material becomes a grid of unmoving negative borons, plus an equal cloud of mobile positive-ionized silicons.
In other words, inside p-type semiconductors, only the "ionization" is moving around, while each positive-charged atom remains locked into the crystal lattice.
Also, take careful note that in physics, "lack of electrons" isn't a thing. (Vacuums lack electrons. Is vacuum therefore made of positive ions? No, that's silly.)
When we say "lack of electrons," we really mean "initially neutral atom, then an electron is removed, leaving an exposed, un-cancelled proton; a positive ion." Holes are actually the un-cancelled protons of the silicon crystal lattice. They really are positive-charged particles. (Only protons can supply positive charge. Missing electrons cannot. "Lack of electrons" just means "un-cancelled protons.") The holes move; the positive ionization moves, but the protons themselves stay still. Like any conductor, the p-type material is overall neutral, (negative borons and positive silicons,) even though it's filled with mobile charges.
Are electrons actually negative ions? Nope.
In the same way that protons aren't positive ions, electrons aren't negative ions. (See, the electrons aren't actually the opposite of holes. Saying they're opposites is just a simplified convenient concept, but not fundamentally true. Electrons are opposites of protons. And negative ionization is the opposite of positive ionization. "Holes" are mobile positive ionizations.)
On the other hand, conduction electrons in n-type semiconductor do create negative ions. Notice that the entire crystal is made of protons and electrons, even though the vast majority of atoms are not ions. All those electrons are part of the valance level; the unmoving bonds between atoms in the crystal. Valence electrons aren't negative ions.
In n-type silicon, each neutral dopant atom, say phosphorous, loses one electron to a neutral silicon neighbor. A pair of opposite charges is created: the boron becomes a positive ion (one un-cancelled proton,) while the silicon neighbor is a negative ion (one extra electron.) Then, the negative phosphorus remains trapped in the lattice, while the "ionization" of the silicon neighbor moves around. This isn't quite the opposite of p-type silicon, because in the p-type crystal, the positive ions were created by exposing the hidden positives inside a previously-neutral atom, rather than by adding positives.
In n-type, both the negative ionization and the electrons are hopping together from atom to atom. Yet at the same time, the entire lattice is made of electrons (neutralized electrons, each one bound close to a proton in the silicon atoms.) The n-type crystal is a group of trapped positive phosphorus ions, immersed in an equal cloud of negative silicon ions created by mobile conduction electrons. Like any conductor, the material is overall neutral, even though it's filled with mobile charges.