Typically the interior part of your HVAC system is the air handler/furnace. This unit (it is tall, so it does look stacked) handles pushing the air around through your ductwork. There is most likely an exterior part to your HVAC system, though, which is the condenser/compressor. The entire unit is almost certainly not housed entirely in your closet. That said, if the unit is operating fine, you may want to reconsider replacement, as it will take many, many years in the condo to pay back based on an upgrade from, say, 9-10 SEER to 14 SEER. There are almost certainly better places to put that money. A better tactic may be to learn to live with it being a little warmer.
Also, consider a seasonal cleaning or maintenance of the unit by a professional if it seems to be operating poorly.
Yes, there is an exterior portion of the unit that is outside. I have a unit on the second floor, so the whole thing resides in a closeted space, while there is a space cut in the wall where the exterior portion is exposed, which should be the condenser/compressor.
The unit up until this past week has been doing just fine. We had some very high humidity days where I am, and the unit was struggling to get back to 78 from the current interior temp of 86 or so. I usually have the system off when were not home. No point cooling the condo down when were gone for 8 hours at work. Since our utility company offers a time-of-use program, we are only charged .05/kw from 7PM-7AM, and all day on weekends. 7AM-7PM however is charged at .30/kw. The unit isn't run during those high peak hours.
I am constantly returning home at 5PM to 80-85 degrees on the thermometer. I kick our windows open and run all our ceiling fans and floor fans until 7, when I then shut the windows and turn on the air conditioning system. (Mind this is only during days where it is this hot.) Within the next 3 hours, around 10PM, the system still hasn't brought the temp down below 83. It is constantly cycling during those hours from what I can tell. I personally can tolerate the temp, but my wife can't.
I feel like I am doing something dumb, since this had never happened the previous year during the summer. (We have been at our residence for a little over a year now.)