Many beginners ask the question: What is the difference between Ippon seoi nage and Seoi nage?
The answer is: 99% of the time when a judo practitioner says Seoi nage they mean Ippon seoi nage.
Ippon Seoi nage means one armed shoulder throw, so this is the full name of the throw. But due to the length of the appellation, the majority of judo practitioners just use the short version “Seoi nage”.
There are other judo techniques finishing with “seoi nage” such as Morote seoi nage which means two armed shoulder throw. But when judo players want to shorten the name of this throw they use the term “Morote” not “seoi nage”.
To sum it up for you, when you hear seoi nage from a judo practitioner, it is the same as Ippon seoi nage.