Yes you can get better at singing.
The last thing you want to do is copy the singer's voice. It will sound unatural as you may of discovered. Instead, try getting 3-5 vocalist you admire, and what you admire of them, try as hard as possible to put it in your voice. This will give you more of that "unique" sound.
It also depends on which genre. For example, with pop-punk, emo, alternative rock you would put as much emotion in your voice as possible.
Listen to different singers voices, and compare the studio version with the live one. If you sound awful, you can see how those singers may have a chance of sounding awful live. The version you may hear on iTunes or the radio is going to sound cleaner, smoother, and clearer than there live performances.
You can get better at singing, and don't give up with it. Try different things with your voice while singing, or just simply get singing lessons. Hopefully I helped out a bit :)
NO-ONE is a born singer! All one has to be able to do beforehand is to carry a tune and the rest will follow during OFFLINE one-on-one lessons with a GOOD vocal teacher. Besides, the best and most honest feedback comes from a trained vocal teacher after an OFFLINE one-on-one audition. Therefore:
Either start saving money for OFFLINE one-on-one lessons with a GOOD vocal teacher, join a choir or find yourself another interest.
In fact, it takes obviously some talent, some luck, LOTS of patience, diligence, courage, hard work, dedication and LOTS of lessons with a GOOD vocal teacher. Besides, your voice will keep maturing until you are in your mid-30s so you need a lot of TIME as well. Therefore:
Sorry, but THE ONLY SAFE way to learn the correct singing techniques & to improve properly IS to take OFFLINE face-to-face singing lessons with a fully trained vocal teacher! The teacher HAS TO BE in the same room with you, so that he/she can give you proper feedback. However, even the best teachers in the world cannot make wonders, so please be realistic with this. Singing lessons are NOT going to help if one is tone-deaf! Please do NOT rely on any dodgy web tutorials because that way you can misunderstand things VERY EASILY and develop bad habits, hoarseness, vocal nodules and other nasties IN NO TIME, and even though you would sound good! It is always much wiser to invest a little bit of your money/time to face-to-face lessons rather than wasting the same amount of money (or even more!) to frequent ear-nose-throat specialist visits due to aforementioned problems, so please reconsider this. If you can't afford vocal lessons, then joining a choir is the only SAFE alternative option. And believe me, but even MANY of those who have music as their hobby DO take lessons as well! Always remember to warm up your voice properly, but please know your limits and don't overdo your voice! Remember the diaphragmatic support, do not strain your throat too much! Also, remember good body posture! Avoid fizzy drinks (burp danger), dairy products (mucus risk), caffeinated products (coffee & tea included, they dry up your throat) and spicy food (irritation risk)! You can consume these things, but NEVER before singing! Do NOT shout, yell, scream nor otherwise abuse your voice AT ANY TIME! Also, please respect your vocal range; if your teacher says you are, say, more of an alto (baritone if you are male), then you ARE more of an alto (baritone).
However: DO NOT try to imitate anyone famous, that will usually give you just bad habits and even damage your throat. You are YOU and your voice is unique, so please learn to cherish that. The world does NOT need copycats.
Do NOT sing, whisper, shout, yell nor scream if having a sore throat/cold/flu, Also, do speak as little as you can if you have flu/cold/sore throat! Remember to drink at least 2 litres of room-temperature still water every day, not just during singing days! Smoking is a big no-no, as is inhaling secondhand smoke. Also, avoid staying in dusty and/or moldy environment.
There you go, leave it or take it, but self-help is as DANGEROUS as trying to perform a minor surgery on oneself after watching how it is done in an episode of Chicago Hope or Holby City. And, sometimes one needs to sacrifice things in order to find the best vocal teacher for oneself.
參考: a student of speech-language-voice therapy