Hi, I'm Nathan.Sorry to hear that you're having trouble with this but I'll do my best to help you.
What is happening is that you are reaching a voicemail service provided by the phone company. It is answering before your home answering machine has a chance to pick up the line, which is why your callers hear a different greeting, and why you get no messages when checking your home answering machine.
The solution in that case is to contact the phone company and have them cancel/remove the voicemail service from your account, OR as an alternative, you could just stop using the answering machine and use the voicemail function instead. You can record your own greeting on the voicemail if you like, and voicemail actually has several advantages: it is always on, meaning it will work even if the power goes out, while the answering machine could stop taking or playing messages if it is ever damaged or unplugged. VM will also work even if you're on another call, with answering machine, the 2nd caller would just get a busy signal. For these reasons, I tend to recommend voicemail over using your own machine, simply because it tends to be more reliable and accessible. The choice is yours of course though.
If you have any other questions, just let me know. Otherwise, please take a moment to rate my service as this is the only way I am credited for my time. Hopefully I have earned 5 Stars but if not please let me know what I can do to ensure you are satisfied. I also invite you to contact me directly with any future support needs at http://bit.ly/1QwLxGh and ask for Nathan.
Thank you, ***** ***** a nice day,