Muscular Endurance:
Your ability to produce maximum force for a maximum amount of time. The force are able to put out will become smaller as time increases. When you increase your muscular endurance, you increase this amount of time that you are able to produce maximum force.
There are two main types of muscular endurance: Anaerobic and Aerobic. Anaerobic is over a short period of time (sprinting). Aerobic is over a longer period of time.
Strength Endurance / Stability:
This is the ability to maintain a high proportion of your strength for as long as possible while also maintaining balance. An example would be during the shoving and holding that go on during a corner kick in soccer. Players who can use their upper body strength to maintain position and balance will have an advantage. This is training the immediate-source energy system.