What happens at rest is that the muscle relies on blood glucose for energy supply. This involves glycolysis, Krebs' cycle and the ETC. In short, glucose is split into two trioses. The two trioses are then completely oxidatively decarboxylated. This produces reduced coenzymes, carbon dioxide and ATP. The reduced coenzymes are reoxidised by the ETC which takes the hydrogens, splits them into protons, that leave into the matrix, and electrons that jump between electron carriers, the last of which is oxygen which unites with protons too to form water. The jumping of electrons generates energy. The energy is used to pump protons from the matrix to the intermembrane space to a certain level. Once this level is reached, electron transport and proton pumping are stopped by ATP synthase and the already pumped protons diffuse through ATP synthase to the matrix. The energy that was used to pump the protons is then used to make ATP.
What happens during excercise is that energy consumption is faster so we need to generate energy faster. We use three mechanisms to do so.
- Phosphagen system
- Aerobic system
- Glycogen-lactic-acid system
The phosphagen system is the one we use first. It relies on the phosphocreatine store. Phosphocreatine can donate its phosphate radical to ADP forming ATP and creatine. This system is short-lived.
When the excercise becomes prolonged, we rely on the aerobic system to maintain higher energy supply than at rest. It's essentially the same as what we do at rest with the exception that we start breaking down glycogen stores to free more glucose. The aerobic system can operate indefinitely; as long as there are enough oxygen and glucose.
If we need more energy than what the aerobic system can provide (more than oxygen supply allows), we start employing the glycogen-lactic-acid system. This system involves glycogen breakdown and glucose splitting into the trioses with no net oxidation and no decarboxylation. This is because the trioses that glucose is split to are oxidised producing reduced coenzymes, but the coenzymes can't be reoxidized by the ETC because there's not enough oxygen supply, so the trioses take back the hydrogens so the coenzymes can be used for another cycle. ATP is only produced at the substrate level. The resulting non-oxidised trioses are lactic acid molecules. Lactic acid, being an acid, causes fatigue, which is gradual reduction in the ability of the muscle to do work.
So to answer your question, yes they happen at the same time.
You can also check this answer for a more in-depth explanation.