Good question! In short, No, soreness is not a good indicator of rest/recovery. And you're right the answer is different for strength training vs aerobic and, if I may add injury. In many cases, with notable exceptions, for aerobic workouts you can usually go by soreness.
Allow me to address each aspect of soreness as soreness can be defined in a number of ways:
- Lactic Acid
- Anaerobic or Micro tears/DOMS
- Aerobic or Cardio
The burning soreness that people refer to is caused by lactic acid buildup as a byproduct of ATP energy breakdown in the muscle cells. The circulatory system cleans the acid out as quickly as it can but just because lactic acid is no longer present, it doesn't necessarily mean that the muscle has recovered.
Strength or Anaerobic:
Soreness can also be caused by micro tears in the muscle fiber, affectionately referred to as ripping by body builders. These micro tears are also called Delayed Onset Muscle Soreness (DOMS). For people accustomed to lifting, they might not notice this as much as others by the time the lactic acid has been cleared out. For people who are new to exercise, on the other hand, they may find it hard to tell the difference between lactic acid, muscle tears, or even crams and spasms. Age is also a factor to consider with DOMS and muscle recovery.
Quote From this article:
"When we experience muscle soreness, commonly referred to as DOMS (delayed onset muscle soreness), we are actually experiencing the chemical response from ours bodies due to the result of the inflammation caused. This inflammation is caused by micro tears of the muscle, where muscle fiber is broken down and needs to be repaired. The inflammation causes the muscles to experience heat, tenderness and they will swell. Don’t be worried by this, as this is a natural response caused by overload, where our body develops so that it can cope if this situation were to arise again."
Recovery can be highly dependent on the individual and the muscle. Given an active healthy person, for strength training it can take up to 7-14 days for the muscle to fully repair and rebuild itself, however, it's generally okay to workout 48-72 hours after on the same muscle group. It is vitally important to give the muscle this time to recover for maximum results and preventing injury.
Cardio or Aerobic:
For aerobic workouts, it depends on the person and the type of aerobic workout. If it's high intensity and/or rough terrain then the rest time will need to be greater. The soreness may be caused by micro tears or lactic acid depending on the intensity. Given an active healthy person, they can generally workout doing to same activity within 24hrs or when they no longer feel the soreness.
Another way of defining soreness is muscle fatigue, cramps or spasms, and pulled and injured muscles. These need to be taken under special consideration and should not be placed under any stress until they have been given proper time to heal. After pain/soreness subsides, immediately engaging in heavy lifts of activities is not recommended at all. Gradually working up to greater weights or activities with caution is recommended. Just how gradual is highly dependent on the severity of injury and the type of activity. I recommend consulting a doctor for specifics.
More reading on DOMS:
More on Lactic Acid: