John Gill Commentary Numbers 5:20

"But if thou have gone aside, being under thy husband, and if thou be defiled, and some man have lain with thee besides thy husband:" — Numbers 5:20 (ASV)

But if you have gone aside to another instead of your
husband
Gone aside from the paths of modesty and chastity, and betook herself to another man's bed instead of her husband's:

and if you are defiled ,
by committing adultery:

and some man has lain with you beside your husband ;
these phrases are all synonymous, and many words are used to express the sin, and that there might be no evasion of it, and that it might be clear what was intended, this being said on oath.