| A transistor is a type of gain stage, very much like a tube only much smaller and much lower-temperature. However most guitarists hate solid-state (transistor) amps because when they are driven into distortion they very often sound terrible, while overdriven tubes sound sweet (and loud). The important thing to remember though is that not all transistor-based amps sound the same--so don't believe anyone who paints them all with the same brush.
A mosfet is a type of transistor; it can be used (and overdriven) in a way that sounds somewhat close to tubes. Look up threads here about the Mesa Walkabout head, as it's a good example of what well-utilized mosfets are capable of, tonally.
The word "digital" is extremely confusing, because most "digital amps" are not really digital--it's just a convenient label that gets misused a lot. A truly digital amp would be one that keeps the guitar signal in a computer data format all the way to just before the speaker output. Some amps have digital preamp stages, for tone shaping and effects, and then an analog (solid state or tube) power section for driving the speakers. And then lastly there's what many bassists are looking at these days, a small/lightweight amp that says it has a "digital power section". In those cases, the word digital is just describing a binary quality to the operation of the power rails: the current rapidly shifts high-low-high-low just like a binary computer signal. However it is NOT a computer signal, and its binary-like nature is not intended to convey information, the way it would in a computer. So when reading about an amp that has the word "digital" in the description, you have to look extra hard at what they mean to find out what -if anything- is digital about it.
Some of the amps by Tecamp, Markbass, Stewart, and other ultralight or "micro" units out there have been described as having a digital power section, so read about those to find out about their various tonal qualities. Note that they don't all sound the same; also note that some micro heads have that type of power section, and some don't. For instance, not all Markbass heads fit that category. | 
