No.
Whey borrow from the private sector, they sell first hand government securities. This is sold under a tender system to basically anyone (people who are willing to buy at the highest price and lowest interest return are sold first until the government can fund its planned deficit.)
In the STMM, governments buy and sell second hand government securities (i.e. they have already been issued - as above - and can be traded) or repurchase agreements.
