SQL Server :: how to move country code column to another table?

Is this what you are looking for?

--demo setup
drop table if exists tbl_Countries;
drop table if exists population_by_country_2020;
go
CREATE TABLE tbl_Countries (
  CountryName VARCHAR(17),
  TwoCharCountryCode varchar(20),
  ThreeCharCountryCode VARCHAR(3)
);

INSERT INTO tbl_Countries
  (CountryName, TwoCharCountryCode, ThreeCharCountryCode)
VALUES
  ('Afghanistan', 'AF', 'AFG'),
  ('Aland Islands', 'AX', 'ALA'),
  ('Albania', 'AL', 'ALB'),
  ('Algeria', 'DZ', 'DZA'),
  ('American Samoa', 'AS', 'ASM'),
  ('Andorra', 'AD', 'AND'),
  ('Angola', 'AO', 'AGO');

CREATE TABLE population_by_country_2020 (
  CountryName VARCHAR(19),
  TwoCharCountryCode varchar(2),
  ThreeCharCountryCode VARCHAR(4)
);

INSERT INTO population_by_country_2020
  (CountryName, TwoCharCountryCode, ThreeCharCountryCode)
VALUES
  ('Afghanistan', NULL, NULL),
  ('Albania', NULL, NULL),
  ('Algeria', NULL, NULL),
  ('American Samoa', NULL, NULL),
  ('Andorra', NULL, NULL),
  ('Angola', NULL, NULL),
  ('Anguilla', NULL, NULL);

-- the solution
UPDATE p
SET p.TwoCharCountryCode = c.TwoCharCountryCode
    ,p.ThreeCharCountryCode = c.ThreeCharCountryCode
FROM population_by_country_2020 p
JOIN tbl_Countries c
    ON c.CountryName = p.CountryName

--verfy
SELECT *
FROM population_by_country_2020

|                |                    |                      | 
|----------------|--------------------|----------------------| 
| CountryName    | TwoCharCountryCode | ThreeCharCountryCode | 
| Afghanistan    | AF                 | AFG                  | 
| Albania        | AL                 | ALB                  | 
| Algeria        | DZ                 | DZA                  | 
| American Samoa | AS                 | ASM                  | 
| Andorra        | AD                 | AND                  | 
| Angola         | AO                 | AGO                  | 
| Anguilla       | NULL               | NULL                 |