Some pumps are designed to be used either way while others are not. Basically a submersible pump is one you can simply stick in the water so the only plumbing you hook up is what feeds out of the pump.
An inline pump is generally placed on the ground next to the tank it is getting water from. Some, designed for above ground pools can't suck water out of a hole in the ground and actually need the water or tank to be higher than the pump but others are designed to actually suction lift water and then push it though the pump even higher.
As to which is more appropriate to your set up will depend on many things. When we are talking really small pumps for systems under say 500 gallons, there is probably not much benefit to an inline pump unless your systems allows for easy placement of your pump next to an above ground tank. And then the only real benefit is that the pump is outside the tank so perhaps easier to access (but you would need valves and unions or flexible couplers around it to make disconnecting it easy.) Submersible pumps are cooled by the water they sit in and it is rarely that difficult to access a pump in your fish tank for a simple small system.
For aquaponics we generally remove the sponge except when you have small fry and just use some sort of grate or basket to keep fish and larger debris away from the pump inlet.
You will want a way to plug in your pump near your system either way, submersible pumps may be more likely to have a long cord but check since they often make multiple versions of the same pump with slightly different features.
My smaller systems all use submersible mag drive pumps and I generally don't start thinking inline pumps till we are looking for something around a flow rate of at least 30 gpm.
The smaller submersible mag drive pumps are going to be more forgiving of being turned on/off by a timer all the time while the larger inline pumps are less likely to handle that kind of abuse and they may be too powerful for a normal home timer to turn on and off (a large motor turning on/off all the time will cause a surge that can burn up little timers that are often meant for turning lighting on/off.)
The most important part of picking a pump is to figure out the flow rate you need at what height and find a pump that fits that requirement or perhaps a bit bigger and then make sure the electrical usage of that pump is efficient. There is a wide range of pump efficiency and the cheapest pump is often going to use a lot more power and probably not last as long as a more costly energy efficient model.
What is the formula to determine flow rate? When you talk about a system being 500 gallons, I'm assuming you mean the total amount of water (ie. water in the fish tank and rafts) in the system. You know I'm considering the Sweetwater SHE 2.4, like the one you use, how do you have yours setup relative to the fish tank. Is it above the tank level? How do you prime the pump? Could I get a submersible mag drive pump that is even more energy efficient than the Sweetwater and still capable of meeting my systems needs?
When figuring out flow rates, generally it is just the fish tank volume we are talking about moving x times per hour. When I talk about my 300 gallon system, that is the fish tank volume. Most raft beds only need a flow of like 5 gpm to keep enough nutrients flowing to the plants and that 5 gpm can be flowing through any amount of raft bed length so the total volume of raft bed water isn't really part of the calculation.
So keep in mind I ALWAYS go for MORE flow and there are plenty of calculators out there that will tell you a lower amount of water flow will be fine and they might be right. That is the disclaimer I tend to go bigger on the pumps because I like lots of water turn over in my fish tank.
So the formula.
The generally recognized rule of thumb for minimum flow rates is to move the volume of your fish tank each hour.
So a 300 gallon fish tank,
you need a pump that will move at least 300 gallons per hour (or if doing timed you will need to move it in whatever part of the hour the pump will be on) at whatever head height you need to lift to. Figure a few extra feet to take into account the resistance in the plumbing and fittings.
So if the surface of the water that the pump is pumping from is 3 feet below the top of the tank or grow bed the water is being pumped too, then I would say look at the pump curve at around 5-6 feet and if the pump will deliver at least 300 gallons at that height then it would meet your minimum requirement.
Now as I said, I like a bit of overkill but you don't want to go too nuts and cost yourself too much extra electricity. Truth is my big system (if it was just a bit more simple without all the extra stuff like towers etc) could probably be running with a 145 watt submersible mag drive pump instead of the SHE 2.4. But since I have all the extra stuff the extra flow is good.
My 300 gallon system is using a Quiet One 4000 and I will estimate that through the indexing valve and with the timing I'm probably pumping 600 gallons per hour in that system.
Could you get a submersible that is more efficient, I'm not sure.
Could you get a submersible that will meet your needs and use less electricity than the SHE 2.4, well I need to know more about your system to know what it's needs are. How big is the fish tank? What will the stocking level be? Where will the pump be placed? How high do you need to pump? What kind of system is it and with what kind of filtration?
So, as to flow rate, I have to move ~700 gal (ie. size of FT) per hour. Since the pump will run continuously, as I plan to use siphons, I need a pump capable of moving 700 GPH at the Head I have (approx 3'-5')? If my math is correct, that is approx 11.6 GPM.
My system is ~700 gal FT stocked with ~100 tilapia, pump either submersed in FT (or inline if SHE ?) pumping to ~100 cubic feet of growbed (either 4 or 6 grow beds totalling ~100 sq ft), which drain via siphons to ~100 cubic feet of raft and from there drain back to the FT. Head is likely between 3' and 5', at a distance of ~25 ft (horizontal distance from pump location, ie. FT, to the growbeds). No sump, no swirl filter, no filtration other than growbeds. I may add towers at some point but not a necessity. Would a submersible pump meet needs and use less electricity than SHE 2.4?
YES there are submersible pumps that will meet your needs and use less electricity than the SHE 2.4.
See at 10' of head, the SHE 2.4 is gonna give about 50 gpm and use about 220 watts.
There is a danner pump (Danner Supreme Mag Drive MD18) that will provide about 15 gpm at 10 foot of head and probably use less than 150 watts. On a side note, this pump can be used submerged or inline if you wish to have it outside your fish tank.
Now the SHE 2.4 may be a more efficient pump overall but if you don't need 50-60 gpm then the efficiency is wasted so for your situation you would be better off using a pump that provides closer to your desired flow rate. The MD 18 is probably a bit of overkill but the excess flow can be used for extra aeration and to have the umph to feed towers later if you need. There is a MD12 but I've not used it and I think you might be cutting it close on flow if you size that close to your minimum needs. The MD18 has 3/4" fittings but I would upsize to at least 1" for the long run out to your grow beds and maybe even 1 1/2" schedule 40 just for the added strength and opacity of the heavier pipe to reduce algae growth inside the long plumbing run. (that's just me, I'm known to keep the plumbing shops in business.)