Although these two words are related, they have very different meanings. The word democracy, for example, refers to a type of government in which power is vested in the people, instead of being concentrated in the hands of a monarch or small group.
There are two types of democracy. In a direct democracy, every person votes on every single decision that is made regarding how society is governed.
In contrast, in a representative democracy, the people vote for people (usually called elected representatives) to deal with administration and governance on their behalf. (This type of democracy is ideally suited to countries with large populations, such as the US, where it is impossible to let every single person vote on every single issue.)
It is in a representative democracy that we find the word "election." An election is a formal process through which the people choose who will represent their interests in government. In essence, there are a number of candidates who stand in an election, and whoever gets the most votes is the winner.