Thanks, Bob, for bringing up an interesting wrinkle to the energy story.

Yes, there is a difference between lactic acid, the product molecule of anaerobic respiration, and lactate. The former carries a H+ proton which is quickly lost at our body's slightly alkaline pH of 7.4. Lactate is simply the lactic acid without that proton.

And yes, muscle cells can use lactate as fuel to generate ATP, because lactate can be converted back to pyruvate, which in turn enters the Krebs cycle again. That process is not only restricted to muscle cells but can play out in other cells, too.

In the liver, it's the Cori cycle that converts lactate back to glucose, as you mentioned. The astrocyte-neuron lactate shuttle (ANLS), while undoubtedly active and of importance for synaptic plasticity and neuronal energy dynamics, is still incompletely understood.

Where I need to clarify a little is the engagement of the glycolytic pathway. Cells strategically switch between glycolysis and beta-oxidation depending on a few key factors, of which oxygen availability is just one. Under anaerobic conditions, the glycolytic endproduct of pyruvate is converted to lactate, but under aerobic conditions (oxygen is available) the pyruvate will enter the mitochondria to be consumed in the Krebs cycle. The other factors that determine the fate of pyruvate are exercise intensity and hormonal influences