You need to do two things - relax & tighten up. I know that sounds a bit confusing, so I'll explain.
Relax - when you're recording, ignore/forget the fact that the recording is happening! It's you either all alone expressing yourself in song, or you're on stage & excited & there's a huge crowd cheering you on cuz you're so well received before you even start. Close your eyes & let it flow out of you. Fear of the recorder will kill your performance if you allow it. Trust me. It happens to a lot of ppl, myself included. Get yourself in a different mindset than the "this is for posterity" thing.
Tighten up - use some good headphones. Set your level roughly equal to if not just a touch louder than the ambient music levels so that you can hear & be sure of your pitch & timing. When you find yourself slipping, don't stop, finish the song as perfect as you can. Do NOT let a slip force you into thinking about your mistake, but continue concentrating on the next note, the next line, & make it so good that your imaginary audience will forget that little slip.
Control these two issues that I'd be willing to bet that you have, & your voice will sound better every time you record it. Ppl often tend to put too much pressure on themselves & then wonder "do I really sound like that?" even though you don't, in actuality, when that pressure isn't there. Remove the pressure. Concentrate on your work. Control the situation.
When you're singing something & your voice just isn't hitting those high notes, listen to the chords of the song & quickly choose a lower harmony note. When you perform live, this will get you by on more occasions than you'd think, & ppl will not even notice the change, more often than not.
One last word - try to hit the notes exactly, rather than sliding into them. That may work for the guy who recorded it, but you need to tighten up before altering your style to something along those lines. Once you are very confident in your work in the areas of pitch & timing, then you can experiment with sliding & other techniques that the pro's use.
Good luck.
