Yes, most training programs will have a mix of short, mid, and long distance running. The shorter distances are speed work that help you develop better form and build muscle strength.
Those mid distances are threshold and pace runs that you run at your half marathon pace to get your body used to the speed at which you will be racing.
The 3 & 4 mile runs are meant to be easy recovery days. They are crucial days for building up your aerobic base, stimulating muscle repair, and giving you an active recovery.
The long days are the critical ones for a half/full marathon. Those are the runs that train your body to run at a fatigued state. You learn what it feels like to be on your feet for 90+ minutes. You learn better mechanics and efficiency. And you just overall stimulate your aerobic system to make you more aerobically efficient.
You need to learn that your body has gears...
Easy pace
Tempo
Half Race pace
5k race pace
Threshold
Full out anaerobic sprints
Ect...
Each of these different gears do different things for your body and stimulate different responses. You need to change up your paces to encourage those effects.
You can't run hard every day or you will break down.
You can't run long every day or you will break down.
You can't run short distances the whole time and expect to run a long race well without it hurting (if you even finish).
Plus there's the whole mental side of things and some days you just need a break. Those short days are there to make sure it doesn't turn into a job.