A lot has been implied about the relative merits of Single Stage, Turret, Auto-indexing Turret and Progressive presses. But implications are less useful than explicit differences.
These thoughts might be useful.
Short answer:
A single stage can only do batch operation, turret can do continuous operation or batch and a progressive only is "natural" doing continuous operation. Single is slow. Turret can be maybe 2 to 4 times as fast and progressive up to 10 or 20 times as fast as a single stage.
Prices: Single stage is $50-$100. Turret is $80-$150? Progressive is $150-$2,000 (these prices are wild guesses, as I have not priced them in a while).
Long answer:
So, you want to jump into reloading. And you have choices.
There are essentially three kinds of presses (but turrets have two sub-categories, auto-indexing or not auto-indexing). They all do the same things, but in different styles. They also do them at different production rates, but it would be a mistake to consider speed alone as your criteria for choosing one press type of anothe
Single stage preesses tend to be (but are not necessarily) stronger and stiffer. This is mostly because single stages' frames are usually of a single casting where all others are of at least two asssembled, moving parts. Since they move, some clearance is pretty much required and introduces some dimensional and alignment variation. In practice, the difference is vanishingly small. But we still argue over it. Progressives have several mating parts which move and have commensurately more play.
In a single stage press, you mount one die and use it to process, one at a time, any number of cases (one "batch") through that die's processing step. Then you dismount that die, mount the next step's die and process the batch through that die's processing step. This is known as "Batch Processing" and is the native way single stage presses work. Pretty much the only way they work.
A turret press is a single stage with the ability to mount multiple dies, but you can still only use one at a time. That is the only physical difference. But that difference allows a turret to do either batch operation or continuous operation at will. This is because you can switch dies as quickly or quicker than you can switch cases. This makes a turret able to process one case from freshly fired to loaded round ready to fire continuously from start to finish or batch like a single stage. Where a turret can do either, a single stage is practical only for batch processing.
Like a single stage, a turret press does only one thing (operation, like size/deprime, belling case mouth, seat/crimp) at a time, but switching between those is nearly instantaneous (especially so with auto-indexing). This makes continuous processing practical.
Batch processing, you are probably familiar with. You can do your batches in 50 as I do or 20 or 100 or 1,000. But the operations are the same. (For pistol) Size/deprime and prime 50 rounds, then switch dies and bell and charge 50 rounds. Inspect the charges in a batch and switch dies. Seat and crimp 50 rounds. Batch is done. Move on to the next batch.
Continuous processing: Put the empty case in the press and do all the operations (size/deprime, bell/charge, seat/crimp) and remove the finished cartridge only when all the steps are done. This saves a lot of handling the cases (at least three insertion-removal cycles) and amounts to a lot of time saved.
If the press indexes the dies automatically, this saves a LOT of time. If you index the die stations manually, it is a little slower, but still much faster than batch processing.
Turret presses can do either batch processing (as a single stage) or continuous processing with nearly equal facility.
Because many loaders of bottleneck (rifle) cartridges do manual operations or inspections in the middle of the loading process, they choose to break up the continuous process into smaller groupings of operations, making the loading process a hybrid of batch and continuous. Other loaders of such cartridges use the continuous process, but temporarily interrupt the process to pull each case from the press before continuing.
Progressive presses can do batch processing, but are designed from the ground up to do continuous processing. It is simply their main reason for being; production rate.
Progressives, by definition do multiple operations simultaneously (except if the operator desires single operation, which can be done). That multiplicity of operation allows producing one completed round with each cycle of the handle. This is true whether the progressive is a 3-station, 4-, 5-, 6-, or 7-station press. Extra stations allow for adding things like a powder-check die or separating the seating and crimping operations, but detracts nothing from the one round per stoke output.
I suggest you view the many (almost too many) videos showing the operation of various presses.
Whatever method(s) is(are) chosen for your new press if the production algorithm is well designed for the cartridge and the user, it will work and is, by design, perfect for them, their temperament and production needs.
Lost Sheep
