The colon is often used to introduce a list of items, for example: You will need to bring three things to the party: some food, something to drink, and a small gift for the hostess.
The semi-colon is often used to join together two independent clauses—in other words, it joins two clauses that could be sentences: Frank drives a Ferrari; Mike drives a Lamborghini. OR: to join two clauses using a transition such as however, therefore, on the other hand, etc.
Source: Style Manual, 6th edition.
Semi-colons should be used to mark a pause longer than a comma and shorter than a full stop. Don’t overdo them. Use them to distinguish phrases listed after a colon if commas will not do the job clearly. Thus, ‘They agreed on only three points: the ceasefire should be immediate; it should be internationally supervised, preferably by the AU; and a peace conference should be held, either in Geneva or in Ouagadougou.’
Source: The Economist Style Guide