So much of what we hear in modern electric guitar tone is shaped by amplifiers and pedals. This can get to be confusing and challenging to understand because are so many options and you have to hear it to understand the differences between different gear and different effects.
Guitar Amps
Guitar amps is a large topic, there simply are so many options. There are vintage style tube amps, modern tube amps, vintage solid state amps, modern solid state amps, modeling amps, pedal amps, cabinet simulators, and on and on.
Tube amps
Many guitarist prefer all-tube amps that use old-style vacuum tube technology to amplify your guitar. These can have amazing tone compared to modern solid-state amplifiers, but they typically are large and heavy, can overheat, are expensive to maintain, etc.
Solid State Amps
Solid state amps use transistors to amplify your guitar instead of vacuum tubes. They are reliable, don’t create heat, don’t need new tubes periodically, tend to be more lightweight. Some of the best modern examples are the Boss Katana and Boss Nexttone, Quilter amps, Blackstar, Marshall, and many more companies make outstanding solid-state or even hybrid tube/transistor models.
Modeling Amps
Modeling amps come in all shapes and sizes. Some are just an amp built into your pedal board that can either go to a speaker cabinet, or right into the PA. Some stages even expect this and have you run your gear right into the PA and use in-ear monitors so there is no stage volume at all (from the guitars). Modeling amps use digital modeling profiles to recreate your favorite guitar rigs including speaker cabinet simulation, effects, etc. These can range in cost and size and include pedals to full size stacks.
This is an ad for Fender amplifiers from 1980. In 1980, many amp manufacturers were switching over to solid-state amps, but Fender continues to product all tube vintage circuit amplifiers to this day. I consider all-tube Fender amplifiers the best sounding amplifiers ever made.