Endurance exercise or aerobic exercise involve activities that make your heart rate and breathing go up, such as jogging, cycling, hiking, and swimming. This type of exercise builds your fitness and keeps your heart, lungs, and circulation healthy. Your goal with endurance training is to keep a consistent effort going over an extended period of time.
Strength training is exercise in which you work your muscles against some kind of resistance like your body weight, bands, or gym weights. This type of exercise increases your muscle strength and size. Strength training involves doing repetitions of a muscle movement with rest periods in between.
Core training involves exercises that specifically target the muscles which stabilize your midsection (i.e., your back and abs). This type of exercise develops a strong core so that you can hold better posture and more efficient form during activities. Core strengthening often involves holding a position steady or doing repetitions of a movement for a set amount of time.
Flexibility/Mobility training includes stretches that lengthen your muscles. This type of exercise improves your range of motion which can help improve sport performance and prevent injuries. Some exercises are static: holding a stretch steady, such as a calf stretch and some are dynamic, like stretching while moving, such as a leg swing.
HIIT involves a warm up followed by very high intensity (maximum!) efforts with moderate efforts in between. Like endurance training, HIIT also makes your heart rate and breathing go up, builds fitness, and keeps your heart, lungs, and circulation healthy. However, unlike endurance training, HIIT involves varying levels of effort, not a steady effort. HIIT is great for people who do not have a lot of time as it offers similar aerobic benefits as continuous aerobic activities.