The very simple answer is; no they are not.
What is the difference?
A sprain is damage to a ligament. Ligaments are the fibrous tissues that connect bones to bones. Many sprains happen suddenly, either from a fall, an awkward movement or a blow. They commonly happen in the ankle, knee or wrist. One example is a misstep, such as falling off a kerb, which could cause you to twist your ankle and lead to you stretching, tearing or even snapping the ligament. The symptoms of a sprain include; pain, swelling, and bruising in the affected area. Additionally, the joint may feel weak and may not be able to bear weight. The severity of these symptoms will depend on whether you have simply overstretched the ligament or if it is torn.
A strain is damage to the tendon. Tendons are the fibrous tissues that connect muscles to bones. Strains are quite often the result of habitual movements or athletics. Athletes who over-train and don't give their muscles enough time to recover in between sessions are at increased risk of such injuries.One example of this would be, what is known as Tennis Elbow which is caused by the repeated contraction of the forearm muscles that you use to straighten and raise your hand and wrist. The symptoms of a strain include pain and swelling and you may experience muscle cramping and weakness.
How to treat a sprain or strain:
The treatment for mild sprains and mild strains is generally the same. Doctors recommend RICE:
Rest. Stay off the affected joint, or try not to use it to allow it time to heal.
Ice. Ice helps reduce inflammation and swelling. Do Not Apply Ice Directly To The Skin! Wrap a thin towel or piece of clothing around a bag of ice (or something frozen - a bag of frozen peas is a common one). Leave it on the affected area for 20 minutes, then remove for 20 minutes. Repeat as much as you can in the first 24-48 hours.
Compress. Compression will also help to reduce the swelling. Wrap the affected joint in a bandage or trainer's tape. Do Not Wrap Too Tightly - this can reduce the blood supply.
Elevate. Try to keep the affected area above the level of your heart to help reduce swelling. If the injury is to your knee or ankle, you may need to stay in bed or on the sofa for up to two days. If you can't manage higher than your heart, parallel to the ground is also ok.
For the first 24 to 48 hours RICE may make you more comfortable and alleviate some signs and symptoms. Move severe sprains and strains, however, may require professional medical intervention or even surgery to repair damaged or torn ligaments, tendons or muscles. You should see a doctor if you experience; difficulty walking or standing without pain, an inability to move or flex the affected joint, or numbness or tingling around the joint.
Helping Prevent Sprains and Strains
Some injuries are not preventable, eg a sudden stumble or whacking your knee, but others are and it is important to take proper precautions to protect your tendons and ligaments.
Warm up before exercising. It is recommended that you do light aerobic activities for about 10 minutes before exercising. One example is walking a lap or two before running round a track.
Start slowly and build gradually. This also helps to warm up your muscles.
Wear shoes that fit well and are made for the sport/exercise you are doing.
Maintain a healthy weight.
Vary your routine. Get a good balance of cardio and strength training. This keeps all of your body fit whilst also allowing you to rest muscle groups
Take a day off after an intense workout session or at least switch to a different activity. This helps reduce your risk for overstretching the same ligaments and tendons repeatedly.
Listen to your body. If you are in pain or feeling tired, rest. Many injuries happen when you are already overtired or stressed.
Stretch. Most experts recommend stretching after exercise, when your body is warm and therefore more flexible. Hold a stretch for no more than 10 to 20 seconds and do each stretch only once. Never bounce or stretch to the point of pain.