I concur with Alphecca. The package example is precisely the difference. Contains comes from a similar root as "contents" which makes it easier to remember that it is speaking of something that holds contents, or can hold in/hold back something example given in the dictionary entry of containing an outbreak. Include more often refers to parts of whole, or a list of multiple items, which is why
contain reminds us a container,so sth. comes within sth else,but include is Seth that could be attached to sth else,so it comes next to sth not necessarily within that