Silver Steel is Water Hardening, though it can be oil hardened and Drill Rod can be W1 (Water hardening) or O1 (Oil Hardening)
Gauge Plate is Oil Hardening both sides of the Atlantic, I think.
Do the details matter? British Standard Silver Steel might be slightly inferior to DIN (German) Silver Steel because the German version adds a bit of Vanadium and tolerates less Phosphorus and Sulphur. W1 is similar to Silver Steel except it has less Chromium and Manganese in it, but adds some Nickel and Vanadium: it's even stricter about reducing Phosphorus and Sulphur. O1 has Chromium and Tungsten in it, and Phosphorus and Sulphur are both forbidden.
The pros and cons of Oil versus Water Hardening are a bit complex. For my simple purposes, water hardening is "good enough" and less mess. Perhaps an expert oil hardener will comment?
Safe enough for amateur purposes to assume Drill Rod and Silver Steel are much the same thing. However, Silver Steel is specialised for ease of use. Simple to harden and gives good performance, but it isn't the best possible tool steel. The Americans seem to include a number of better alloys under the 'Drill Rod' banner, but they're not so straightforward to use as W1 and O1.
Dave