I've been looking into batterie's datasheets and don't understard what 2 of the specifications mean: continuous standard current and maximum continuous discharge current. Could someone explain this to me?
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Standard discharge current is related with nominal/rated battery capacity (for example 2500mAh), and cycle count.
If battery is discharged with higher current - real available capacity will be smaller (it may be much smaller). Discharging battery with lower current will extend real available capacity a little bit.
Currents higher than standard will shorten battery life, lower will extend it (in comparison with nominal cycle count).
Maximum continuous discharge current is a current that will not overheat and destroy battery, but keep in mind that discharging battery with maximum allowed current will reduce battery life significantly and probably real available capacity will be less than nominal.
Here is an example, where you can see how battery capacity changes at diffrent discharge currents
There is no information about maximum discharge current, however it looks like that battery can be discharged with 850mA, but you can't use whole 1.3Ah capacity.
Another example - Sanyo AAA Eneloop NiMh rechargeable battery:
Continuous standard current sounds like "nominal" drain current, what current does the manufacturer expect to be a typical load under ordinary usage, probably much less than the maximum. In general you might expect this number to be something like 1/5 or 1/10 of the C rate, meaning a 5 hour or 10 hour time to fully discharge.
Maximum continuous discharge current sounds like what is the maximum drain current that will remain safe on the battery without "abusing" it and thereby shortening battery life. Probably they state "continuous" as a way of saying DC or quasi-DC current, meaning it's OK if current spikes above the "maximum" for very short periods of time, e.g. milliseconds but not seconds at a time, especially if buffered by a large bypass capacitor.