cycle use: 14.4-15.0V(25 degree Celsius): This is the maximum voltage supplied by the charger to the battery for overnight charging. Modern chargers will reduce this voltage after the charge current drops below some level. Leaving the battery under "cycle" charging voltage for long, will reduce its service life due to gassing.
initial current: less than 1.35A: This is the maximum charge current that the battery may accept. So if your charger delivers more current, you cannot use it for this battery as this may damage the battery.
Standby use: 13.6-13.8(25): This is the recommended charge voltage that you may apply for very long time. This holds for applications where the battery is used as a back up. The main supply in the device using the battery backup keeps the battery at this voltage. So when there is a power faillure, the battery is fully charged. Charging with this voltage takes longer (then using the "cycle" voltage levels), but secures maximum service live in standby operation.
12V4.0P/20HR: Very likely: this battery is 12V, has a capacity of 4Ah when discharged over a periode of 20 hours. In this case, this means discharging with 0.2A. What is the size of it? As it may also mean 12V 4A for 20 hours (so a 80Ah battery).
Note that leaving lead acid batteries uncharged will distroy them for sure (sulfatation). Note that actual charging voltage should be corrected for temperature. The Lower the temperature, the higher the charge voltage should be for efficient charging. check your batteries on regular intervals. A fully charged lead acid battery, left alone for some days (that means no charge no discharge for some days) should read about 12.8V on your voltmeter. When it drops below 12V, you should charge the battery for sure.