The two main brands available are ReplayTV and TiVo. It's generally been replaced by DVD, but it still has its fans. Only a few companies make the discs or players. Gaining in popularity is Hi8, an 8mm format with better resolution. Since laser is involved, it's called burning.
CD recorders can be part of a home computer or a stereo system.
Make sure it's a CD-RW drive. If it's CD ROM, it only reads discs, not records them. It means compact disc recordable. It's a CD that can be recorded only once. A CD-R can be played on almost all CD players.