No. At its most "basic" level:
WAR = (Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment + League Adjustment + Replacement Runs) / (Runs Per Win)
If your head hasn't exploded lately, take a look here, and it will...
Calculating Position Player WAR, A Complete Example | Sabermetrics Library (fangraphs.com)
There is more here:
What is WAR in Baseball? How To Calculate War In Baseball (scottfujita.com)
The best part? Different places use different calculations, so there can be different results for the same player...