The difference between a battery charger and a battery tender is that the charger will keep applying current to the battery all the time, day after day. This is bad on the battery.
A battery tender applies a very small current and is designed to shut itself on and off depending on battery voltage.
What's rough on your battery is allowing it to sit for a week, 2 weeks, etc. without any charge at all. As I mentioned, when a current is not being applied (charger, alternator, etc.) the battery is sulfating, whether it's a day, week, or month. Sulfating is a way of saying the battery is going stale if you want to look at it that way.
An alarm system could drain it over a period of weeks, especially if the battery is marginal. With winter coming on I would have the battery load tested since cold weather requires more current to crank and start the car.
A proper load test means at least 30 minutes (preferably an hour) on the charger followed by application of a high current load with a carbon pile. Battery voltage at the end of the test should be at least 10.2.
If you're not very mechanically inclined you may not understand that part, but if someone is doing a proper load test they SHOULD be familiar with it.