Terminology:
"Silver solder" actually means silver
braze (a filler alloy melting over 800F/427C). A typical formulation being some Zn and Cu, with more than half (the balance) Ag, and melting over 1300-1400F (the mushy range is intentional; brazes tend to be used to fill gaps). Yes, it bothers me too, but alas, this is what it's called. If you call it silver braze, I don't think you'd confuse anyone, and should prefer to call it that to try and clear up this nonsesnse.
"Solder" (otherwise unqualified) means a low melting (white metal) alloy, i.e., below that temp.
What you have is a silver-
bearing solder, i.e., regular solder, but it's bearing some dissolved silver.
Likewise, there are many kinds of silver-bearing solders; for example, Tektronix used to hide some inside their (vacuum tube era) equipment, since the 3% Ag content made it less likely to dissolve the silver metallization on the ceramic terminal strips they used.
But among lead-free, SAC is the most likely alloy, yeah.
(Similar confusion exists for FETs, where the constant current region of operation is "saturation". We should really just forget about that one, too.)
Topical chem joke as your reward for reading this,
http://www.lab-initio.com/screen_res/nz063.jpg Tim