On land rover discovery handbook, it says need group size 24 battery, why in all battery stores say I need group size 34?

The size numbers you are referring to- 24 and 34, refer to the BCI group number of the battery. These numbers define the physical dimensions of the battery case- that's it!

It has nothing to do with the CCA [cold cranking amps rating] or AH [amps per hour rating], or the battery life.

BCI stands for Battery Council International; it is a trade association of manufacturers of original equipment (OEM) and after-market auto batteries. This association is responsible for setting the standards and testing dimension and sizes of lead acid batteries.

So, to sum it all up, the BCI 24 battery has the following dimensions: its Length 10.3" (260mm); Its Width is 6.8" (175mm); and its Height 8.9" (225mm)

The BCI 34 battery has the following dimensions: Its Length is 10.3" (260mm); Its Width is 6.8" (175mm); and its height is 7.9" (200mm)

Both batteries have the positive polarity on the left hand side and are located on the top of the battery; they are for automotive use and are SAE (Society of Automotive Engineers) approved standards.

The difference between the two batteries are in their dimensional height; the BCI 24 is 8.9'' whereas the BCI 34 height is shorter at 7.9" by 1".

As long as the battery tray and the battery hold down clamps can secure the BCI 34 in place, you should have no problems.

HOWEVER, should you decide to buy the BCI 34, make sure the CCA rating is the same or more than the BCI 24; that's where it counts the most in cold weather. And of course, the reserve Capacity rating (RC).

Never compromise the aforementioned by going with lower ratings when replacing a battery to save a few bucks, because it will cost you more money in the long run when having to call for AAA services or replacing the battery again because of its short life due to energy demands that automobiles of today command as a result of all the electronic components that are used during the operation of the vehicle or the paralytic draw (slow power drain of the ECM and its components) when not in use.

The 24 battery is a better battery in that it has a charge acceptance of 200 amps, an amp hour rate of 80 and a cca ( cranking rate) of 800
the 34 battery is a slightly smaller batter with an hour rate of 50 but the cca is the same (800)
The manufacturer recommends a 24 battery so I would stay with that recommendation
go on google and type in batterystuff.com and read the qualities of the various batteries
basically the bigger capacity AMP.hr and the bigger CCA battery is prefered as it cranks longer and holds full voltage under cranking longer