Thanks for the replies, everyone! I did a test, calling my phone from my work line, and the volume button does indeed work to immediately silence the phone, AND it keeps ringing for the caller. Oddly, for my test, it rang SIX times on the land line before my galaxy even started ringing... and it rang at least six more times on the landline before it went to voice mail. I'll have to look into that--must be a setting somewhere...
In the past I was using call end and had a complaint that I was "hanging up" on them! The silent ringtone idea doesn't really work for me as there are various callers where I want to send them to voice mail quickly.
Thanks again! When I bought this phone (my first Smartphone) friends and family were advocating the iphone, but that just wasn't flexible enough for me. So far the galaxy is great, although I feel I've explored only a tiny part of it. Glad this forum is here.