It may be described as vertical bat shots where the bat is swung vertically at the ball or horizontal shots where the bat is swung horizontally at the ball.
While a batsman is not limited in how he may hit the ball, the development of good technique has gone hand in hand with the development of a standard or orthodox cricket shots played to specific types of deliveries.
Vertical Bat Strokes
Vertical bat strokes can be played either with the front foot or the back foot depending upon the anticipated height of the ball when it reaches the batsman. The position at the point of contact is usually aligned vertically. At this point, according to the facing of the bat, the shot can be either block or defensive, glance or deflection or a drive.
On taking a long stride, the batsman can block the ball with a forward defensive shot. This block stroke is a defensive stroke to stop the ball from hitting the wicket or touching the batsman's body. A block played on the front foot is known as a forward defensive, while that played on the back foot is known as a backward defensive.
The application of the block strokes can be sometimes even used to score runs using it as a base to move the ball into the rather emptier portions of the field which is then termed as a push.
A leg glance is a delicate shot that relies more on the pace of the ball to make it go to the boundary. It's a straight-batted shot used to flick the ball requiring skilful wrist work. If the ball is pitched at the toes, it is played off the front foot but if the ball bounces at hip height then it's played off the back foot.
A batsman usually plays a cover drive off the front foot.
A Drive is one of the most common shots of a batsman and is often the first shot that is taught to cricketers starting out. A drive is again a straight-batted shot executed by swinging the bat in a vertical arc through the line of the ball. Depending on the direction in which the ball moves, a drive can be a cover drive, straight drive or a square drive. There also exists a "midwicket drive" that is played towards a midwicket. Drives can be played both of the front and the back foot.
A flick shot is also a straight-batted shot executed by flicking a complete-length delivery using the wrists. The shot is played with the bat coming through straight as for the on drive, but the bat face is angled towards the leg side. It can be played both off the front foot or the back foot, whether it's from the toes or from the hips.
HORIZONTAL BAT STROKES
Horizontal bat shots are also known as cross bat shots which include the cut, the square drive, the pull, the hook and the sweep. A lot of times, horizontal bat shots have a bigger probability of failing to make contact with the ball when compared to vertical bat shots. Its usage is therefore restricted to deliveries that do not threaten to hit the stumps.
A cut is a cross-batted shot ideal for a short-pitched ball. A batsman plays a cut with the back foot although it can be sometimes played off the front foot against slower bowling. The batsman makes contact as or after that ball passes him and therefore requires no effort on his part. A square cut is hit into the off side, 90 degrees from the wicket
A late cut stroke is attempted as or after the ball passes the batsman's body and then hit towards the third man.
Although this shot is named a "drive," which can be confusing, a square drive is a horizontal bat stroke with exact arm movements of a square cut. The difference is only at the height of the ball in contact with the batsman. On a waist height ball, a cut is played whereas a square drive is played to a ball at shin height.
Pull and Hook
A pull is a cross-batted shot executed to a ball around waist height by swinging the bat in a horizontal arc. The hook shot is played when the shot is played against above the chest height of a batsman. Pull and hook shots can be played off the front or back foot, with the back foot being used more commonly.
A sweep shot is only played by a left-handed batsman. It is a cross-batted front foot shot executed to a low ball, usually by kneeling on one knee and swinging the bat around in a horizontal arc. Usually, the sweep shot is played to a leg-side delivery. Attempting to sweep a full straight delivery on the stumps is generally not recommended.
With this, we've more or less talked about all the different types of bat strokes that can be executed by the batsman. Now it's upto you to practice and master the different batting techniques.