1) "Intervals", as I understand it, refers to the recovery interval, between repetitions.
2) The purpose of the workout(s) can vary ... I'll get to that ... but,
Actually, I think you are asking the question backwards, if as you say, you are trying to decide what workouts to do. Probably better to start by understanding what you are training for, where you are in your training, and the components that should be included in this part of your training. Then use that information to determine the purpose of each workout that will go on your schedule.
This will be rudimentary bc I am not an expert- apologies to anybody who knows more than I do, if I say something dumb here--
Ok, let's say you are training for, say, the mile, and you have periodized your 6-12 mo training cycle into, for example, Base Phase, Intensity Phase, Competition Phase, and Peaking Phase. Suppose you have completed Base training, and your Intensity Phase is going to have, say, two workouts per week. Let's say the objective of your Intensity Phase is to maintain / further develop the aerobic fitness you developed during Base Phase while also developing speed & strength needed to prepare for the harder workouts & races during the upcoming Competition Phase.
Ok, so in this example maybe you decide that the purpose of the first workout is for aerobic threshold training. Let’s say you did 20' tempo runs during Base Phase, so maybe you decide to do 1200m cruise intervals during Intensity. You determine the appropriate pace (a little faster than tempo runs), the number of reps (say, 5, for a workout volume of 6000m; that is, more than your tempo run distance during the previous training phase), and an appropriate rest or recovery for this type of workout, given its purpose (in this case, I dunno, say 60 sec 200m jog).
All right, let's say the second workout is speed/strength. Suppose you opt for 8 x 400m. Say you did a mile TT at the end of Base Phase, so you know your current fitness. Since you know the purpose of the workout, you can structure it according to its purpose - maybe you decide that the speed component is key during this phase, so you decide to run the first 6 reps at 1-2 sec faster than TT pace, then faster for the last two; also, given the purpose of the workout, perhaps a slow 3 min 400m jog plus 30 sec standing rest will allow you enough recovery to maintain quality of pace during the session (let's say you're planning on reducing recovery time during the next training phase).
In this example, suppose all your other days are easy runs and one long run. Now, you can look at the plan and see if anything is missing. Hmmm ... maybe you figure that, for you, it will be difficult to significantly improve those 400m repeats without some other, faster sessions. But you don't want to add another workout, bc you already have 2 workouts and a long run, and you know you can't handle a third workout without causing problems for yourself, and you don't want to remove anything that's already in your weekly schedule ... ok then, maybe you decide to add some strides / 4 x 75m accelerations to the end of your easy runs. Just enough to get you a little turnover, not enough to wear you out over several weeks of this training phase.
Hopefully that example made sense. Knowing the purpose helps you determine the workout. Asking it the other way, without any context, may not make as much sense.
For example, what's the purpose of 8 x 400? I don’t know. The question has no context and doesn't make any sense by itself. What pace/effort are the 400s at? What kind of rest or recovery? For a marathoner, 8 x 400 with 800m jog might be the fastest top-speed workout they do. For a 10K runner, 8 x 400m at race pace with 2 min standing rest might be an easy stride-out session a day or two before a race. Shorter/longer recovery intervals with varying efforts are all totally different workouts with totally different purposes.
Likewise, 1200m repeats can have a variety of purposes. If, say 3-4 reps at threshold effort with 1 minute jog, the purpose may be to help you get fit enough to eventually do a full 15-20 min tempo run. If more reps at slightly faster than tempo pace with a short recovery jog, the purpose may be to give you more threshold work than a 20' tempo run. If done at something like 2-mile pace with equal time or half time recovery, it is probably a VO2max session. As another example, in college I was given 1200m repeats at "sustainably hard" effort, with standing rest to HR 120, at a progressively faster pace over a few weeks, as part of fall training for 400m. The purpose was aerobic development.
tl;dr The purpose can vary, depending on the specifics. When deciding on a workout, first know the purpose/objective and then plan the workout accordingly.
Gahh. That was long. Sorry for the dang book. Hopefully, I wrote something sensible.