All digital guitar amps are at least partially solid state, but not all solid-state amplifiers are digital. If that sounds confusing, don’t worry, it’s actually very simple:
A solid-state amplifier has a solid-state (transistors, resistors, capacitors, not tubes) preamplifier that produces the tone of the guitar amp, and then has a solid-state power amp circuit that amplifies the signal and drive the speaker(s). A classic example of a solid-state guitar amplifier is the Roland JC-120 Jazz Chorus; there are many other examples, as well.
Digital guitar amps use digital algorithms to produce the tone of the amplifier. Line 6, Peavey, and Vox are among the many manufacturers who make digital guitar amps. Theoretically, the tone could then be amplified either via a tube or solid-state power amp. Indeed, there are amplifiers such as the Line 6 DT line of amps that have digital front ends and tube power-amp sections.
But the majority of digital guitar amps integrate solid-state power sections — that way, the digital algorithm can emulate the tone of various tube power amp stages and the solid-state power section can amplify that tone cleanly.