What is the difference between 将来 and 未来？
I was told that 未来 is further in the future than 将来. Is this true?

Not necessarily:

我将来要买辆车。-- Several years.
我将来要成为音乐家。-- Several decades.
人类将来会灭绝。-- Several millennia, to be optimistic.
宇宙将来会热寂。-- Several billion years, probably.

In these cases 将来 works as adverbs, it can be used for the most distant future. You can use 未来 in all these examples, but it would sound slightly pretentious. So if you are doing adverbs, 将来 is often be a better choice.
If you use 将来 and 未来 as nouns, then it's a different story. Here 未来 do seem to mean a more distant future:

台湾的未来究竟会怎样？-- Sung by Zheng Zhi-hua.
教育要现代化，面向世界，面向未来。-- Said by Deng Xiaoping.
在不远的将来……-- Idiom.
在遥远的未来……-- Idiom.

The thing here is 将来 is seldom used as a noun. I could hardly think of an example besides the one above.
Let's talk about adjectives. When you use 未来, you often imply something big or grandeur. 将来 is less so, and sounds slightly less formal. The difference is not big and in many cases you can use them interchangeably:

未来的汽车不需要人驾驶。-- 将来 means the same but sounds more casual.
美国是我们将来的合作伙伴。-- 未来 may sound more formal but 将来 is also OK.
你是我未来的妻子。-- 将来 sounds less formal. You want to treat your marriage seriously, so 将来的妻子 is less idiomatic.

未来 is used together with another noun to form futuristic concepts, as in 未来世界, 未来城市, 未来时代. The 的 can be omitted. The same doesn't apply for 将来. In fact if you want to use 将来 as an adjective, you should always add 的 in between.