There are two major types of SMD capacitors.
This type:

which are used primarily for small values and tight locations

and this type:

which are used for larger values

It appears that the two sets of pads are for the two types of capacitors: the wider pads for the square ones, and the thinner/longer pads for the can style. If you can find the value that you need in the can style, it should work fine as long as there are no physical requirements.
As for using non-surface mount capacitor... dont. You will likely end up with a really messy result that has a high risk of shorting on somethings else, or even worse, ripping the pads off the motherboard if it catches on something. Just go through the trouble to solder new SMD caps. Try cleaning the pads, and then apply a small solder bead to the bare pad. Use tweezers to place the component on the pads, then touch the iron to each side to let the solder flow onto the component. If you don't have hot tweezers, that is the easiest way IMO. Or you could use solder paste, but it is rather expensive.

I wouldn't be considering non SMD caps. Would SMD MLCCs or Tantalums work instead of the SMD electrolytics, and which one would be better?

It ultimately depends on the application of the capacitor. In most applications that an electrolytic would be used, you can replace it with a tantalum. Ceramics do have some different behavioral aspects than electrolytics, so even if the capacitance is the same, it might not behave 100% normally. I would stick with the tantalum.

Polymer caps can now be used for much of the range of SMD electrolytics and are a good substitute for tantalum caps as well.

In the mass-production world, shit happens.

When you need to make 10,000 widgets and suddenly a specific part isn't available, you are screwed. So it is common to include multiple pads for different but compatible pieces when you can expect shortages of certain parts.

The manufacturer ran out of 100uf smd caps? Well just slap in an electrolytic on an adjacent pad. Boom, your order gets fulfilled and you get a bonus for having things to sell when there is a parts shortage.

look at this video card: http://www.vgamuseum.info/images/zaatharen/nv … _model2_fhq.jpg

Those memory pads under the installed memory are there for the same reason your caps have 2 sets of pads. Its just in the video card's case they had a backup plan for a different memory chip that had a different pin-out.

gdjacobs wrote:

Polymer caps can now be used for much of the range of SMD electrolytics and are a good substitute for tantalum caps as well.

I know those exist for the Can types, but do you mean these specifically? https://uk.farnell.com/c/passive-components/c … ymer-capacitors

The PAD is part of the PCB under-lament. Part of the copper trace network. If the PAD is gone which is common when capacitors burst and leak acid onto the PCB board. Then you need to get some thin copper sheeting and cut out a NEW pad and trace line to repair. You need to glue down the NEW PAD to the PCB board and solder the new copper PAD trace line to the PCB board trace. Requires cleaning the PCB and scraping off some of the trace protective coating and then glueing on a NEW PAD and soldering the end to the original PCB trace line.
You need special glue and PCB trace shielding laminate.
And a microscope for sure as this is micro surgery.
And once you have the PAD and trace repaired then you can solder on a NEW capacitor.

https://youtu.be/vx50YtEC2S8

Thanks. I'm aware of what they are, and they're all fine.

sirlemonhead wrote:

I know those exist for the Can types, but do you mean these specifically? https://uk.farnell.com/c/passive-components/c … ymer-capacitors

Panasonic has polymers in 2917 plastic packages.

Here's the app note where they delve into replacement options.
https://www.element14.com/community/docs/DOC- … ts-for-tantalum