I think you might me mixing up a few different historical periods. The Russian Empire as it existed (which fell in 1917) is not described as "Soviet." Or, at least, not by anyone who is vaguely familiar with it.

"Soviet" is used to describe the Union of Soviet Socialist Republics, also known as the USSR and the "Soviet Union." The USSR was a collection of Soviet Republics, the most prominent of which was the Russian Soviet Federative Socialist Republic. The other nations that made up the Soviet Union had their own Soviet Republics (there were 15.)

The Soviet Republics formed after the October Revolution of 1917. The term "Soviet" itself referred to worker councils - governing bodies that sprung up in the early 20th century, and formed the governing structure of Soviet Russia immediately after the October Revolution. "Soviet" itself is an older term, basically meaning council.

So, "Soviet" is used to describe the Soviet Union and the Soviet Republics because, well, it's in their name.

Soviets is a loose catch-all term for worker's and soldier's councils that mushroomed in Russian cities during the collapse of the tsarist state during the Revolutions of 1917. These Soviets became very important to municipal politics and became a thorn in the side to the Provisional Government. The 1917 Soviets often saw themselves as heirs to the worker's councils that briefly appeared during the Revolution of 1905 when tsarist state authority had seemingly collapsed and were determined that 1917 would not repeat the earlier failed revolution. The Provisional Government sought to limit the influence of radical Soviets and other leftists groups that were taking advantage of the power vacuum created by the destruction of state authority. The Bolsheviks were able to capitalize upon the Provisional Government's animus directed against the Soviets when they seized power under the slogan "all power to the Soviets." From the civil war onwards, the Bolsheviks presented themselves as the head of a revolutionary coalition that was operating in the name of the Soviets, who were the expression of proletarian organization in Russia. Behind the scenes, the Bolsheviks either co-opted or purged many of the independent political elements within the Soviets. When the Reds emerged victorious in the Civil War in 1922, the Bolsheviks called their new state the Soviet Union, to reflect an alleged ideological diversity that had been achieved under the aegis of the Communist Party of the Soviet Union.

The best source for the jockeying for power amidst the evaporation of the tsarist state and its Provisional Government successor is Alexander Rabinowitch's trilogy on 1917 (Prelude to Revolution, The Bolsheviks come to Power, and The Bolsheviks in Power).