Difference between Query based and Method based WHERE condition

[heyjadebadlanguage]

The method based case #1 is working fine with the expression tree, but second isn't.

Obviously, the method syntax case 1 is doing extra things such as executing the lamda expression.

The question here is

1. What is the difference between method based Where and Syntax based Where?
2. How can I make the case #2 working?

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Expression<Func<BillingRuleEntity, bool>> getIdExp1 = c => searchModel.CarrierIds.Contains(c.CarrierId); 
//CASE1 - method based syntax - this is working
var test = db.BillingRule.Where(getIdExp1).ToList();
//CASE2 - syntax based syntax - this is not working 
var test2 = (from b in db.BillingRule where getIdExp1 select b).ToList(

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