Most road bikes today come with integrated brake and shifting levers, or brifters. They are more comfortable and usable than traditional styles. Let's look at some available options.
Shifting mechanisms
Shifters work by increasing or decreasing the tension on the shift cables to move the derailleur into place.
Indexed
Indexed shifters click into place and move the derailleur one gear. They allow for precise shifting, but need to be tuned and parts are made for specific speeds and derailleurs. Brifters are all index shifters.
Friction
Friction shifters just tighten or loosen the cable to shift, you have to adjust it by feel - or by ear if you can hear the chain rubbing. You need to adjust the tension on the shifter to keep the cable from slipping but still allow you to shift, which is why it's called friction shifters.
Shifter types
These shifter types can use either of the shift mechanisms described above, and some can do both.
Downtube shifters
These bolt on to braze on mounts on the downtube, or clamp on adapters. One advantage is that you can quickly shift through multiple gears with a quick flick of the lever. However, you have to take your hand off the brake and bars, and can get tedious with frequent adjustments.
Stem shifters
These are basically downtube shifters, mounted on the handlebar stem. This is more convenient for an upright rider with their hands on top of the bars instead of in the drops.
Thumb shifters
These are like downtube and stem mounted shifters, but designed for flat bars and positioned to use with flat bar brake levers. Some people are using them today for retro builds or gravel bikes.