The SS-18 uses different engines from the Zenit. Those Zenit engines might be derivatives of the SS-18 engines, but I have not had a chance to research it. If the engines are significantly different, then the rockets are different. The Zenit SL3 uses an RD-171 engine in the first stage. The SS-18 uses the RD264

One key difference is that the SS-18 uses hypergolic propellants, while the Zenit engine uses kerosene/LOX. Doesn't sound at all like the same booster to me.

From the SS-18 Mod 1 (R36m) specs on Encyclopedia Astronautica (with some significant parameters highlighted:

Manufacturer: Yangel. Launches: 145. Failures: 14. Success Rate: 90.34% pct. First Launch Date: 22 October 1971. Last Launch Date: 17 April 1997. Launch data is: incomplete. Liftoff Thrust: 400,000 kgf. Liftoff Thrust: 4,500.00 kN. Total Mass: 209,600 kg. Core Diameter: 3.00 m. Total Length: 33.60 m.</b< Span: 3.05 m. Standard warhead mass: 7,250 kg. Maximum range: 11,200 km. Number Standard Warheads: 1. Standard RV: 15B86. Standard warhead yield: 24,000 KT. Standard warhead CEP: 0 km. Maximum range with alternate warhead: 9,250 km. Number Alternate Warheads: 8. Alternate RV: 15F143U. Alternate warhead yield: 500 KT. Alternate warhead CEP: 0 km. Boost Propulsion: Storable liquid rocket, N2O4/UDMH. Boost engine: RD-264. Cruise Propulsion: Storable liquid rocket, N2O4/UDMH. Cruise engine: RD-0228. Cruise Thrust: 77,000 kgf. Guidance: Inertial.

From the Zenit 3SL page:

Stage Number: 1. 1 x Zenit-1 Gross Mass: 354,300 kg. Empty Mass: 28,600 kg. Thrust (vac): 834,243 kgf. Isp: 337 sec. Burn time: 150 sec. Isp(sl): 311 sec. Diameter: 3.90 m. Span: 3.90 m. Length: 32.90 m. Propellants: Lox/Kerosene No Engines: 1. RD-171 Status: In Production. Comments: Modification of same stage used as strap-on for Energia launch vehicle.

Let's see, it appears the Zenit's first stage has twice the liftoff thrust of the SS-18 Mod 1. The length and diameter are different, too. While it's possible that later models of the SS-18 had different first stage specifications, at least from this comparison it doesn't look like they're the same.