Man, you don't know how big a topic that question brings up...
First of all, assault weapon and assault rifle are not equal terms.
An assault rifle is:
1) an individual shoulder-fired military weapon
2) chambered in an intermediate caliber
3) fed by a detachable magazine
4) that is also select-fire (semi-auto, burst, full-auto, etc).
Since your SKS is not select fire and most do not have a detachable magazine (it sounds like yours may have that feature), it is not an "assault rifle." Neither is a common AR-15 variant or semi-auto Kalashnikov.
Assault weapon is a term created by politicians to encompass more firearms and vilify them. An assault weapon is semi-automatic, accepts detachable magazines and has at least two of the following characteristics:
1) folding or adjustable stock
2) pistol grip
3) bayonet or bayonet mount
4) flash suppressor or threads to accept one
5) grenade launcher
6) barrel shroud (also known as "the shoulder thing that goes up
With the features that you described, yes, your SKS would have fallen under the 1994 Assault Weapons Ban. However, that ban expired in 2004 and the political environment was such that it was not reinstated. It also was shown to have very little effect on crime rates and basically only had an impact on the legal selling of scary looking firearms (see EBR below), mainly outlining cosmetic features
Some states have chosen to continue the same rules as the 1994 ban.
Many people fear another ban being legislated. If another ban is passed some day, it likely will not resemble the past ban in the slightest, but will be much more restrictive and probably including regulation of ammunition.
Most firearms owners choose not to use the term "assault rifle" or "assault weapon" due to them being loaded phrases and carrying a lot of political baggage. Others have embraced the terms either to try to take them from the politicians who use them in a negative way, or to look macho. If you really look at the terms, a baseball bat or a hammer can be an assault weapon.
Other people propose terms such as Sport Utility Rifle, Civilian Sporting Rifle, Civilian Defense Rifle, Evil Black Rifle (EBR), etc.
Personally, I call my XCR Bam Bam and it has never assaulted anyone.