Question on AC Adapters for rechargeable devices (particularly a laptop)

[tappybot]

This question actually concerns a laptop I'm purchasing from the US, and having shipped to Japan.

Here's the information for the battery on the website:

6 Cells Lithium Ion Battery Pack (62.16Wh)
Full Range 90W AC-In 100-240 V AC, 50/60Hz Universal  |  DC Output: 19V, 4.74A AC Adapter
*120W AC Adapter included with 3rd Generation Intel® Ivy Bridge Core™ i7-3610QM upgrade

My question is, are these adapters made for the US and Japanese regions identical?  It says 100-240 V AC, as if you could use said charger would be the included product anywhere in the world.
I worry because I feel like my old laptop, which I'm using now in Japan, has gotten it's battery run down by a charge that's not strong enough.. that's my feeling anyway.. I have to leave it plugged in or the battery's dead within 20-40 min.

I was going to ask if adapters for devices like Nintendo DS's are the same, but having just examined my US region DS's adapter, and my Japanese 3DS's adapter, the info on the back looks about the same.

So is there anything I should be concerned about??

Thanks!

[133MHz]

My question is, are these adapters made for the US and Japanese regions identical?  It says 100-240 V AC, as if you could use said charger would be the included product anywhere in the world.

Exactly. Switching power supplies nowadays such as laptop chargers are truly universal - they work anywhere in the world and adjust to the line voltage automatically within a very wide range of tolerances.

I worry because I feel like my old laptop, which I'm using now in Japan, has gotten it's battery run down by a charge that's not strong enough.. that's my feeling anyway.. I have to leave it plugged in or the battery's dead within 20-40 min.

Lithium-Ion batteries degrade over time whether you use them or not. 
A faulty or underpowered charger wouldn't charge your battery at all and it would have a hard time just powering your laptop.

[80sFREAK]

Batteries, made in close neiboroughood with volumerates-or-whatever-their-name will degrade faster, so that sort of folks created lots of stories about laptop batteries. Such as "take off battery, if you running on wall plug". Wake up there is smart  charge controller in each battery and if Mao's kids forgot to install one, it will make nice firework

The matter is output of PSU and jack tofit your laptop.