Both words are verbs; however, their meanings are different. Exceed comes from the combination of cedo with the prefix ex, which means forth. Accede was formed by placing the ad prefix meaning toward or at least together with cedo. These words were ultimately adopted into English with different spellings and pronunciations. When the word accede is used, it will be followed by the word most of the time.
The context is somewhat restricted for the word accede since it is generally employed in political or another official context. On the other hand, exceeds means to be greater than some specified limit, which can be good or bad.
For example, something could end up better than you expected. You could also say that exceed is used when telling someone how much of something they can have.
For example, “Do not exceed two packages of bottled water.” This direction implies that the supply of bottled water does not exceed the demand for it. Therefore, everyone is relegated to just two.