Type 430 = S43000. A ferritic SS, commonly used for automobile trim. Composition 16-18% Cr, 1.00% Mn (max), 1.00 % Si (max), 0.12% C (max), 0.04% P (max), 0.03% S (max).
Type 430F = S43020 is a free-machining version with 0.15% S (min.),
Type 430F 'Solenoid Quality' (also S43020) is another free-machining grade, "the chemical composition and processing of which are controlled within precise limits to assure consistently high magnetic permeability, low coercive force (Hc) and low residual induction (Br), while offering corrosion resistance similar to that of standard Type 430F stainless." The composition differs somewhat & includes 17.25-18.25% Cr, 0.25-0.40% S, 0.60 % Ni and 0.50% Mo
Type 430FR 'Solenoid Quality' (no UNS that I can see). As Type 430F 'Solenoid Grade' except lower C 0.065% (max) & higher Si: 1.00-1.50%.
Info from Carpenter Stainless Steels - Selection - Alloy Data - Fabrication.
I presume the 'Solenoid Quality' (no UNS) grades are proprietary, but there should be other suppliers with their own 'Solenoid Quality' products. I see no reason to use these grades except for solenoids or other electromagnetic applications, as the high S content reduces corrosion resistance.