What is muscle pain?
Muscle pain is pain originating from the muscle tissue and related connective tissues.

What is nerve pain?
Nerve pain is pain originating from the brain or spinal cord (the central nervous system), or the peripheral nerves that branch off from the brain or spinal cord, like the sciatic nerve down the back of the leg or the nerve endings in the fingertips and toes.

Causes of Muscle Pain:
Common reasons muscle and soft tissue may be painful are tightness or spasm, overuse and fatigue, trauma to the tissue, or inflammation. Some chronic illnesses, viral or bacterial infections, and certain medications can also lead to muscle and soft tissue pain.

Causes of Nerve Pain:
Nerve pain can be caused by damage to the nerves or inflammation irritating the nerves. In the central nervous system, this may occur due to many reasons such as stroke, multiple sclerosis, spinal cord injury, or tumors. Peripheral nerves may become painful due to damage caused by disease like diabetes, alcoholism, vitamin deficiencies, viruses (shingles, lyme’s disease), direct trauma to the nerve (disc herniation, surgery, injury), and chemotherapy or radiation. Dysregulation of the sympathetic nerves can cause complex regional pain syndrome (CRPS).

What does muscle pain feel like?
Muscle pain can feel like aching, throbbing, stabbing, pulling, or tearing. Pain may be fairly constant or vary greatly depending on activity or position.

What does nerve pain feel like?
Nerve pain feels like burning, shooting, electric shocking, tingling, hot or cold water running down skin. Nerve pain is often reproducible by placing the nerve under stress with activity such as walking for a certain distance, causing pain to spread down the leg. Positions like tipping the head to one side can also cause pain to spread
down the arm  or cause a stimulation like shower water hitting the skin of the foot causing burning.

Treatments for Muscle Pain:
Everyone experiences acute muscle pain at times–think of the sharp tearing pain of pulling your hamstring. This kind of pain is best treated with activity modification, ice and heat, and over the counter anti-inflammatories, acetaminophen, and topical medications. Many people develop chronic muscle pain–think of the constant pain of tight neck muscles felt when working on a computer or after a severe whiplash. This kind of pain is best treated with physical therapy and/or a daily home exercise and stretching regimen. There are often other underlying conditions of the joints or nerves that are contributing to the reaction in the muscle. These conditions may need to be addressed with minimally invasive procedures such as trigger point injections, epidural steroid injections, or radiofrequency ablations before the physical
therapy will be tolerated and the muscle pain will resolve.

Treatments for Nerve Pain:
Nerve pain can be acute, like the sudden onset of sciatic pain down the leg with a lumbar disc herniation. It is important to protect the nerve from permanent damage by reducing the pressure on the nerves. Treatment of acute nerve pain often involves oral or injected steroids to reduce inflammation. Sometimes, surgery is needed to prevent acute nerve pain from becoming chronic if other measures don’t work and especially if numbness or weakness is also occurring. For diffused nerve pain such as occurs in diabetic neuropathy, it is important to stop the underlying cause to prevent worsening. Blood work is often needed to look for reversible causes of neuropathy like high blood sugar or vitamin deficiencies that could be treated. Certain anti-seizure drugs like Gabapentin and Lyrica and certain antidepressants
like Amitriptyline and Duloxetine work well for chronic nerve pain. Procedures such as radiofrequency ablations or implanted devices like nerve stimulators are useful in some cases. A combination of treatments including medications, therapies, procedures, and counseling is the most effective.

https://my.clevelandclinic.org/health/symptoms/17669-muscle-pain

https://my.clevelandclinic.org/health/diseases/15833-neuropathic-pain

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5371025/