Yes ^^^
There are two types of 12volt batteries.
Regular car batteries and Deep cycle batteries
Regular car batteries can provide high amps quickly, for cranking starter motors, but are damaged if they are discharged too much, they have thin plates inside which allow for quick high amp discharges but deteriorate faster when used for long steady drains.
Deep cycle batteries have thicker plates, so can't provide the high amps as quickly, but are better at long steady discharges.
Deep cycle can still crank starter motor, and Regular battery can be used for long discharges, it's just that each has a specific purpose it was designed for so...........
Deep cycle would be best choice as 2nd battery, for running lights and stereo or ?? while engine is off.
It doesn't bother isolator or alternator to have the 2 different types of batteries, they are just 12volt batteries in that respect.
There are new "hybrid" batteries that claim to have the high amp discharge and the long drain ability, and if you were only running one battery I might suggest trying one of these.
But I have always found that "hybrids" are not "the best" at two things, they are a compromise so are just "OK" at two things, which isn't bad.
If running a 2nd battery I would look at getting a deep cycle.
Welcome Visitor! Please take a few seconds and 
