There are many ways to express the same thought - many more than you might realize.
Vocabulary
The first thing is the difference between active and passive vocabulary, also known as productive and receptive knowledge. You may recognize a word and its meaning when reading it, but you may not use that word when talking or writing yourself. It's just a word that you have used so few times that it wouldn't cross your mind to use this word.
To take an example from a recent discussion here on Writers.SE (How to talk about certain anatomy without sounding vulgar or cowardly?): you may understand the word Gluteus Maximus and what part of the body I am alluding to, but using a medical term in a normal conversation wouldn't cross your mind. Using posterior on the other hand feels more natural, though in general I would probably use butt. Your usage will probably vary. Maybe because you like medical terms, or because you don't like defensive descriptions like posterior.
To cite the Wikipedia article I linked before:
An average 20-year-old knows 42,000 words coming from 11,100 word families
Now you have to ask yourself: how many words are there in total?
According to the Oxford dictionary:
It's also difficult to decide what counts as 'English'. What about medical and scientific terms? Latin words used in law, French words used in cooking, German words used in academic writing, Japanese words used in martial arts? Do you count Scots dialect? Teenage slang? Abbreviations?
It's not that easy to find out how many words there are. And the number changes all the time because people are creating new words and older words are slowly forgotten.
But to give at least a rough idea the link also contains the following phrase:
The Second Edition of the 20-volume Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries.
Using these very simple statistics we can say that the average 20-year-old knows about a fourth of the currently used words in the Oxford English Dictionary.
But you have to adjust this number: the german article about vocabulary mentions that the standard vocabulary contains around 75,000 words - while the total is estimated to be somewhere around 500,000 for everyday conversations. If you are taking into account specialised terminology this number goes up into the millions, with the example of chemistry having probably around 20 million words.
The average 20-year-old may have a pretty good grasp of the normal everyday language and know quite a lot of those words and he may understand a good amount of stuff that he wouldn't use himself, but there are so many more words in the world that he never heard about that it's unrealistic to say that he will have the same style of talking and writing as his peers.
The bottom line is that you are probably vastly underestimating the amount of words that your native language contains. The active vocabulary of you, your friends and your family may be similar, but if you are asking a different group you may find huge differences, just because there are so many possibilities. 312
The same applies to sentence structure and other parts of writing.
You also asked about example - take a look through this answer. I tried to hide a few different ways of speech here.
Did you catch the difference in referring to other sources? In the third paragraph I linked another question and paraphrased the content. Afterwards I changed to citation from Wikipedia and other sites. It's not unreasonable to see this as one part of my voice. Am I using a lot of paraphrasing or citations? Or a mixture? How much paraphrasing sounds good? There are some grey areas here, allowing for different voices if you just compared this simple attribute throughout the site.
Sentence length
The easiest thing to express different voices is through the use of longer or shorter sentences. Look at your own post: I can clearly see that you prefer longer sentences. You used a lot of commas and and's to extend your sentences and except for your last paragraph each paragraph contains exactly one sentence and is at least 1.5 lines long. Your last sentence would only be half a line, which is probably why you didn't bother making it a paragraph of its own.
I also like long sentences. Most of the time, at least. Sometimes shorter sentences are better. They are easier to understand for the reader.
But then again, longer sentences may sound more eloquent, which might be the desired effect when writing. This completely depends on your target audience - are you writing for younger people, who may have problems following long, complicated sentences, or academics who seem to have a knack for this kind of sentence structure?
Punctuation
Did you realize how often I use dashes and colons to split a sentence and at the same time continue the thought? 873