sql - Getting strange reaction in T-SQL script

Question

I am writing a stored procedure and when I tested the procedure in Execution Plan/Sentry Plan Explorer I have noticed that in one statement the plan reacts strangely.

Here are 2 scripts that from my point of view are the same, but the results are significantly different.

Script 1 (not real code, but a code that demonstrates the problem):

DECLARE @MyVariable INT;
SET @MyVariable = 123456789;

SELECT MT.Name, OT.Name
FROM MyTable MT
INNER JOIN OtherTable OT ON MT.ID = OT.MyTableID
WHERE OT.TypeID = @MyVariable;

Script 2:

SELECT MT.Name, OT.Name
FROM MyTable MT
INNER JOIN OtherTable OT ON MT.ID = OT.MyTableID
WHERE OT.TypeID = 123456789;

It seems to be the same, but the results I get are different:

1. Estimated rows in Script 1: 15621 rows (wrong for sure, too many rows)
2. Estimated rows in Script 2: 205 rows (logical result, probably true)

I think that the SQL execution plan behaves differently when a variable is used in the where clause. Why? Or what is going on here? How to improve this?

Thanks