Colons and semi-colons can both be used in lists, but in different parts of the sentence.
A colon is used to introduce a list if the first part of the sentence makes sense on its own.
I have three best friends: Neela, Josie and Karla.
If the first part of the sentence doesn't make sense on its own then a colon is not used.
My three best friends are Neela, Josie and Karla.
Semi-colons can be used to separate items in a list if the items consist of more than one word.
I need to buy two tins of tomatoes; a leg of lamb; a sack of potatoes; and three pints of milk.
On our cruise we went to Athens, Greece; Naples, Italy; Malaga, Spain; and Nice, France.
Commas could be used instead for the first example above, as the list would still be easy to understand. However, if commas were used in the second example it would look like eight different places instead of four.
A colon can also be used to introduce a quotation or direct speech if the first part of the sentence makes sense on its own.
My nanna has a favourite saying: "Look after the pennies and the pounds will take care of themselves."
Again, a colon should not be used if the first part of the sentence does not make sense on its own. A comma is used instead.
My nanna says, "Look after the pennies and the pounds will take care of themselves."
Semi-colons are never used to introduce speech or quotations.