Differences between "foreign key" and "constraint foreign key"

The first one assigns a user-defined name to the foreign key, the second one will assign a system-generated name to the foreign key.

User-defined foreign key names can be useful for subsequent statements like these:

ALTER TABLE XTable DROP    CONSTRAINT fk_idq;
ALTER TABLE XTable ENABLE  CONSTRAINT fk_idq;
ALTER TABLE XTable DISABLE CONSTRAINT fk_idq;

It's harder to alter constraints with system-generated names, as you have to discover those names first.

The first option is purely for naming the constraint.

From SQL FOREIGN KEY Constraint

To allow naming of a FOREIGN KEY constraint, and for defining a FOREIGN KEY constraint on multiple columns, use the following SQL syntax

CREATE TABLE Orders
(
  O_Id int NOT NULL,
  OrderNo int NOT NULL,
  P_Id int,
  PRIMARY KEY (O_Id),
  CONSTRAINT fk_PerOrders FOREIGN KEY (P_Id)
  REFERENCES Persons(P_Id)
)

Also, from CREATE TABLE (Transact-SQL) one can see that [ CONSTRAINT constraint_name ] is optional.