I see this misused so often that I thought perhaps a more concise explanation might help.
The Engy mod (part of the base FAF game, not an actual mod) makes two types of factory upgrades available at Techs 2 and 3. When you upgrade your first factory to T2 (land, air, or naval, the concept is the same for all three) it automatically becomes a HQ factory. Once the first HQ factory is complete then a new upgrade button unlocks in all T1 factories of the same type. Meaning that once a land factory is upgraded to T2 all other T1 land factories gain a new upgrade option. This upgrade I am calling the “support” factory. The tooltip simply calls it T2 factory (as opposed to T2 HQ). The support factory upgrade is substantially cheaper and faster. In addition, once you have a HQ factory then each tech level engineer can then build a corresponding tech level support factory. So once you have a T2 land HQ then T2 engineers can build a T2 support land factory (skipping the upgrade step). The same concept applies at T3.
Below are the actual numbers based on the in game tooltips. I only tested UEF and Seraphim but found them to be almost the same so I assumed that all factions were identical (or meant to be).
Land
T2 HQ
Mass: 800 Energy: 7200 Time: 1:20
T2 Support
Mass: 300 Energy: 2700 Time: 1:05
Engy T2 Support
Mass: 540 Energy: 4,800 Time: 1:44
T3 HQ
Mass: 3,400 Energy: 30,600 Time: 4:35
T3 Support
Mass: 750 Energy: 6,750 Time: 1:15
Engy T3 Support
Mass: 1,200 Energy: 11,500 Time: 1:40
Air
T2 HQ
Mass: 630 Energy: 11,600 Time: 1:30
T2 Support
Mass: 300 Energy: 5,571 Time: 1:05
Engy T2 Support
Mass: 510 Energy: 7,971 Time: 1:44 (bug?)
T3 HQ
Mass: 3,250 Energy: 85,091 Time: 4:20
T3 Support
Mass: 1000 Energy: 26,182 Time: 1:40
Engy T3 Support
Mass: 1,510 Energy: 34,153 Time: 2:13
Navy
T2 HQ
Mass: 1,370 Energy: 6,600 Time: 2:00
T2 Support
Mass: 500 Energy: 2,500 Time: 1:40
Engy T2 Support
Mass: 800 Energy: 4,000 Time: 2:40
T3 HQ
Mass: 5,450 Energy: 24,472 Time: 2:33
T3 Support
Mass: 800 Energy: 3,429 Time: 1:06
Engy T3 Support
Mass: 1,600 Energy: 7,429 Time: 2:13
As you can see you would be crazy to spend extra resources on more than on HQ (barring a possible strategic choice – see below). Upgrade one factory to HQ to get the unlock and then all subsequent upgrades should be the cheaper and faster support factories.
The HQ factory and the support factory are identical in terms of performance. They can build the same units at exactly the same rate at exactly the same resource consumption. The only real difference is that a support factory has ½ the HP of the HQ factory.
There is one important drawback of the support factory. It must have an existing HQ factory to continue production at that tech level. If the HQ factory is destroyed then the upgraded support factory will only be able to produce T1 units until a new HQ factory of corresponding level is rebuilt. This could lead to the strategic choice I alluded to above. Since all of your support factories are dependent on the HQ factory then it might be a strategic choice to have a second HQ factory in order to avoid the “all your eggs in one basket” issue.
Hope this is helpful.