That's a pretty good overview, MW.
Here's the more detailed explanation. First, to address whether a spacecraft can control its speed on reentry - yes, but they usually don't. It costs considerably less to build a heat shield and let the Earth's atmosphere slow you down than to build a powered flyback system that slows the spacecraft, as you would need to bring along extra fuel to do this.
There are different reentry trajectories for different missions as well. The three basic categories of trajectories engineers use are gliding, skip, and ballistic.
If I recall, the Space Shuttle follows a skip trajectory where it actually bounces of the atmosphere once to bleed of speed before it reenters on a basically gliding trajectory. This trajectory has the lowest peak heating rate but the highest overall heat absorbed (it's in the atmosphere the longest). This is exactly what the ceramic tiles on the Space Shuttle are designed to do, absorb a lot of heat over a relatively long period of time.
Capsule designs generally follow a gliding reentry path (similar to the last part of the shuttle reentry path). During the descent, the capsule is usually inclined at some angle of attack to produce lift. This decreases the total acceleration load as the spacecraft remains in the upper atmosphere for a longer period of time and also decreases the peak heating rate, although not as much as the skip reentry.
Ballistic reentries are usually used for things like ballistic missiles or probes that require the least amount of heat flux. This trajectory is characterized by the the spacecraft (or missile) producing no lift. The spacecraft experiences the highest peak heating rate compared to the other two trajectories, but it also experiences the lowest total heat flux as it is not in the atmosphere as long.
So depending on the mission requirements and the design of the thermal protection system, any of these three trajectories can be chosen.