Resolution Issue when connecting Laptop to Monitor via HDMI cable

Hey everyone, I'm having this problem with Dota 2 and Diablo III. Whenever I connect my approximately 15" laptop to my 24" monitor using an HDMI cable, it forces me to use a lower resolution in order for the game to not be laggy. When I use my laptop by itself, it can support the highest resolution which is like 1324 x 1024 or something like that, in addition to all the highest settings (except shadow), and the game looks perfect. However, when I connect it to my monitor, there are many more resolutions to choose from, the highest being 1924 x 1000 or something, but when I choose this resolution the game LOOKS like it does when I just use my laptop at the 1324 x 1024 (or something close to that) resolution but it plays much much slower and forces me to use a lower resolution such as 1024 x 800 in order for it to be playable at the cost of graphics. I'm just wondering because when I play other games on my laptop that's hooked up to my monitor the games I play look the exact same on the monitor as they do on the laptop and I'm not forced to use a lower resolution, such as HoN. But when I play dota 2 and Diablo 3, the graphics become shittier on my monitor because I am forced to use a lower resolution. I don't need or want a higher resolution supported by my monitor if using it only makes the game laggy and unplayable, I'd rather use the lower resolution of my laptop with the perfect graphics and have it displayed in that exact way onto the monitor, which is what happens with other games that I play, namely HoN. Do I need to configure my display settings in any way to get the exact image from my laptop onto my monitor? Or do I need to use a VGA cable instead of HDMI or something? Or is that I simply cannot have the same graphics displayed on my laptop (15") be copied exactly onto my monitor (24") due to graphics card reasons? This is what I thought at first but I can play HoN with the best graphics available on my monitor as well as my laptop. I'm not extremely tech-savvy so explaining my situation might sound a little confusing for some so I tried to explain it as best I could. Any help is appreciated, thanks. I just thought that using an HDMI cable should copy the exact image on my laptop onto my monitor as it does when I'm simply surfing the Internet or playing HoN.

Flangdoogler, welcome to the Seven Forums.

The full make and model of your laptop would help, as then we could see what it has for graphics in it (GPU). Depending on what it is it is likely that you answered your own question,

Or is that I simply cannot have the same graphics displayed on my laptop (15") be copied exactly onto my monitor (24") due to graphics card reasons?

If the graphics card in the laptop isn't up to running it at high settings and resolution, then one or the other has to be lowered (and most time both) to get the game to be playable.

I'll check the model of it tonight when I get home but it's pretty new and runs Diablo 3 (a brand new game) on the highest possible resolution and settings (except shadow setting, which I don't care about) on my laptop, it's only when it's hooked up to the monitor that it lags on the highest resolution (the 1924 x 1000 one). I've updated my drivers and such and the graphics card is an integrated ATI 6000 series I'm pretty sure, but again, I'll let you know exactly tonight. For now, though, is there any setting that I can alter to get an exact image of my laptop onto my monitor? When I connect my laptop to my monitor it seems as though it shows the exact image until I close my laptop lid, then it adjusts the monitor to a higher resolution. I've thought about playing with my laptop lid open just to see if it is an exact image but it isn't, it's actually a lower resolution on the monitor so that might be evidence of the fact that my graphics card simply can't run it that well on the monitor. I still want to know if there is a setting I can change to show the exact image, like somewhere in the Control Panel or Display settings so I can just mess around with it, I'm just unaware of where to start. Thanks for the reply dude.

OPERATING SYSTEM:
Windows 2.6.1.7600
CPU TYPE:
Intel® Core™ i5 CPU M 480 @ 2.67GHz
CPU SPEED:
2.69 GHz
SYSTEM MEMORY:
3.8 GB
VIDEO CARD MODEL:
ATI Mobility Radeon HD 6370
VIDEO CARD MEMORY:
2.14 GB
VIDEO CARD DRIVER:
atiu9pag.dll
DESKTOP RESOLUTION:
1280x800
HARD DISK SIZE:
666.93 GB

It's a HP Pavilion dv6-3375ca Rossignol Special Edition Entertainment Notebook PC and I've updated all my drivers including video and BIOS