You are correct. Conscription and the draft are essentially the same. I believe conscription is when you enter military service regardless of wartime, while the draft is explicitly to fill ranks. I could be wrong on that though.
>Are you suspecting that the law would be changed to enable draft?
Yes, if we get into a large scale war without the ability to recruit enough volunteers, most certainly. Currently our recruiting numbers are way down. The US has had a draft/conscription throughout most of its history. Current times since 1973 are an anomaly.
Also, the law is already in place. Every male citizen, when they turn 18 must register with the Selective Service, which is responsible for the draft.
However, conscription remains in place on a contingency basis; all male U.S. citizens, regardless of where they live, and male immigrants, whether documented or undocumented, residing within the United States, who are 18 through 25 are required to register with the Selective Service System.[2][3] United States federal law also continues to provide for the compulsory conscription of men between the ages of 17 and 44 who are, or who have made a declaration of intention to become, U.S. citizens, and additionally certain women, for militia service pursuant to Article I, Section 8 of the United States Constitution and 10 U.S. Code § 246.[4][5][6]
https://en.wikipedia.org/wiki/Conscription_in_the_United_Sta...
In fact, reinstitution the draft is required by law:
A national emergency, exceeding the Department of Defense’s capability to recruit and retain its total force strength, requires Congress to amend the Military Selective Service Act to authorize the President to induct personnel into the Armed Forces.
https://www.sss.gov/about/return-to-draft
The term for a person who pushes for war without any intention of serving themselves is called a Chickenhawk. I'm just reminding all the people who are pushing for escalation with Russia that if war happens, they will likely be drafted and aren't just sending the mostly poor kids to fight their war. To those people I say, be careful what you wish for.