Combining Tables in MySQL
Yes, it is possible to do. There is a CREATE TABLE ... SELECT clause in MySQL that is designed specifically for that. I recommend you start with a simple SELECT statement that clearly defines what the new table would contain. E.g. if you have a mammals table:

CREATE TABLE mammals (
     id MEDIUMINT NOT NULL AUTO_INCREMENT,
     name CHAR(30) NOT NULL,
     PRIMARY KEY (id)
) ENGINE=MyISAM;

INSERT INTO mammals (name) VALUES
    ('dog'),('cat'),('whale');


and a birds table

CREATE TABLE birds (
     id MEDIUMINT NOT NULL AUTO_INCREMENT,
     name CHAR(30) NOT NULL,
     PRIMARY KEY (id)
) ENGINE=MyISAM;

INSERT INTO birds (name) VALUES
    ('chicken'),('duck');


You can build this query:

SELECT name FROM mammals
UNION ALL 
SELECT name FROM birds;


The result will contain all animals. However, you may need to keep the animal type in the new table. Modify the query like this:

SELECT name, 1 as type FROM mammals
UNION ALL 
SELECT name, 2 as type FROM birds;


and create a new table

CREATE TABLE animaltype (
     id MEDIUMINT NOT NULL AUTO_INCREMENT,
     type CHAR(30) NOT NULL,
     PRIMARY KEY (id)
) ENGINE=MyISAM;

INSERT INTO animaltype (type) VALUES
    ('mammal'),('bird');


Now, when you are completely happy with the result execute:

CREATE TABLE animals AS
SELECT name, 1 as type FROM mammals
UNION ALL 
SELECT name, 2 as type FROM birds;

ALTER TABLE animals ADD COLUMN id INT AUTO_INCREMENT NOT NULL PRIMARY KEY;


Optionally:

DROP TABLE mammals;
DROP TABLE birds;


You can also create a foreign key for the animaltype.type column