Most animals (actually not only the animals but most eukaryotic cells) can produce energy (in the form of ATP) by transforming glucose into lactic acid, exactly like in the lactic fermentation of milk into yogurt.
(Some animals and some other eukaryotic organisms use other fermentation variants, e.g. alcoholic fermentation by yeasts or fermentation of glucose + water into acetic acid + carbon dioxide + dihydrogen in cells with hydrogenosomes.)
The energy produced thus is many times lower than the energy that could be produced by oxidizing the same quantity of glucose into water and carbon dioxide.
While the energy is low, the power is very high, because the fermentation is done by a simpler sequence of reactions and a much larger quantity of glucose can be fermented in a given time than the quantity that could be fully oxidized.
So the difference between using glucose fermentation and using the oxidation of either glucose or fat is like the difference between using supercapacitors and using batteries.
Some devices are optimized for high power but lower energy storage capacity, while others are optimized for low power but much higher energy capacity.
In most cells there is a more complex hierarchy of energy-producing mechanisms, which are ordered from the highest power and lowest energy capacity to the lowest power and the highest energy capacity. For example, in the muscles of vertebrates, you have, in the order from above, ATP hydrolysis, phosphocreatine hydrolysis, glucose fermentation and finally glucose & fat oxidation.
The vertebrates are actually much better than most other animals at glucose fermentation, which gives them a significant advantage.
Because of that, the vertebrates are able of short bursts of activity that use a very high power, e.g. running short distances or jumping or catching a prey, before having to reduce the power to the lower level that can be sustained for a long time by the aerobic oxidation.
Just to reiterate one key part for your question, all of the energy systems (ATP hydrolysis, phosphocreatine hydrolysis, glucose fermentation and finally glucose & fat oxidation) can produce energy in tandem and/or independently in muscle and other cells. But, first listed higher power systems are depleted within minutes and require expense of other systems to "recharge" (supercapacitor analogy) vs. glucose & fat oxidation can pretty much carry on constantly but are much lower power due to slower speed/higher complexity of their pathways (rather than just a battery I'd say an analogy of renewable energy [glucose] + battery storage [lipids in adipose] is more suitable i.e. steady input of energy source = steady utilization/output of work that can carry on pretty much constantly).
So, many systems can produce energy together/in tandem in the cells, but the higher power systems once exhausted can force your body to temporarily cease high intensity activity to rest and recover. Glucose and fat oxidation don't ever stop in that process, but in recovering those higher power systems your body prevents you from engaging in more high energy "burst" activities until those systems "recharge".
Training can allow you to modify these higher power systems to last longer, and recover quicker, but there will always be a top end constraint where every person "runs out of gas" when performing continuous high intensity/exertion activity.
(Some animals and some other eukaryotic organisms use other fermentation variants, e.g. alcoholic fermentation by yeasts or fermentation of glucose + water into acetic acid + carbon dioxide + dihydrogen in cells with hydrogenosomes.)
The energy produced thus is many times lower than the energy that could be produced by oxidizing the same quantity of glucose into water and carbon dioxide.
While the energy is low, the power is very high, because the fermentation is done by a simpler sequence of reactions and a much larger quantity of glucose can be fermented in a given time than the quantity that could be fully oxidized.
So the difference between using glucose fermentation and using the oxidation of either glucose or fat is like the difference between using supercapacitors and using batteries.
Some devices are optimized for high power but lower energy storage capacity, while others are optimized for low power but much higher energy capacity.
In most cells there is a more complex hierarchy of energy-producing mechanisms, which are ordered from the highest power and lowest energy capacity to the lowest power and the highest energy capacity. For example, in the muscles of vertebrates, you have, in the order from above, ATP hydrolysis, phosphocreatine hydrolysis, glucose fermentation and finally glucose & fat oxidation.
The vertebrates are actually much better than most other animals at glucose fermentation, which gives them a significant advantage.
Because of that, the vertebrates are able of short bursts of activity that use a very high power, e.g. running short distances or jumping or catching a prey, before having to reduce the power to the lower level that can be sustained for a long time by the aerobic oxidation.