Concentric

Concentric muscle action means that the muscle is shorthening

Eccentric

Eccentric muscle action means that the muscle is lenghtening

There are various terms used to more specifically describe different types of contractions, below you can find the definitions of the most commonly used.

Isometric exercise (Constant length)

During isometric exercises muscles contract, however there is no motion in the affected joints. The muscle fibers maintain a constant length throughout the entire contraction. Isometric training is effective for developing total strength of a particular muscle or group of muscles. It is often used for rehabilitation since the exact area of muscle weakness can be isolated and strengthening can be administered at the proper joint angle. As you can see the principle of specificity also applies here. In this example with regards to joint angle.

Isotonic exercise (constant load)

Isotonic exercise differs from isometric exercise in that the contraction causes a joint to move. A classic example of an isotonic exercise is weight training with dumbbells and barbells. As the weight is lifted throughout the range of motion, the muscle shortens (concentric) and lengthens (eccentric). The load stays the same troughout the range of movement. (Although variations in load will inevitably occur due to the changing length of the lever arm to the fulcrum)

Isokinetic exercise (constant speed)

In isokinetic exercises the speed is constant no matter how much effort is exerted. Such exercises are used to test and improve muscular strength and endurance, and are most commonly utilized by professional athletes. This type of exercise requires rather expensive equipment.