Okay. You probably already get it now, but I'll try and lay out the information as clearly as I can.
In Fates (as in most Fire Emblem games) the maximum character level is 40.
However, there are base classes and promoted classes. In your base class, you can level up to 20. Once you reach 20/-, you stop gaining exp.
You then have to use a Master Seal to promote. Once promoted, you become level 1 in the promoted class (20/1) and can carry on leveling up to 20.
Master Seal is solely for promotion. So for example, if you promote at level 15, you miss out on 5 levels' worth of stats. In very niche cases such as high difficulties, you might benefit from the additional base stats you get from promoting, but 90% of the time you want to wait until 20.
Basically, leveling is linear. You can't "de-level", but using a Master Seal will put you at level 21 (Lv. 1 promoted), even though you can use it starting from level 10.
After Master Seal,
every other seal type except for Eternal Seals can be thought of as a sideways move. Your level will not change nor will you promote, you will just change into another class.
Most times when using a Master Seal you can pick from 2 classes. Therefore when using, say, a Heart Seal, after you have already promoted, you can select from the promoted options for both your base class and your alternate class. Same thing applies for Marriage and Friendship seals (you can choose from both class options).
Some classes are special classes that level up to 40. This is mostly Songstress and the DLC classes (Dread Fighter, Dark Falcon, Lodestar, Great Lord, etc.) In these cases you won't need to promote, but if you try to switch classes at level 21 or higher, you will be able to change to the promoted classes.
The Eternal Seal is separate in that it adds 5 to a character's level cap. So with 1 seal you can level to 45 (25 in a promoted class), etc. They're mostly intended for postgame usage especially as they're so expensive.
It's
not possible to miss out on skills. If you Heart Seal into another class, you will gain a skill on your next level up if you are high enough for it. Example: As a level 12 Hero, you switch to Swordmaster. At Level 13 you will gain Duelist Blow and then at 14 you get Vantage. (15 Astra, 16 Swordfaire).
The only way it's possible to "miss" skills is if you hit the level cap of 40 before you're able to learn all skills for a class, e.g. you switch to Great Lord at level 37, then you will learn the next 3 skills at 38, 39 and 40 but will "miss" out on Awakening at level 40. You can still learn this by using an Eternal Seal and going to 41 however (but it will be pricey).
Also worth noting is that each class has its own individual growth rates, which are added on to a character's base growth rates to get the total growth rates for a unit. For example Sorcerer has +25% to Mag and +10% to Spd, but 0% in HP and 0% in Str. As such it would be bad for a physically orientated character to remain in this class beyond picking up any desired skills.
I hope this makes sense.
"Perfectionism becomes desirable when it stimulates the healthy pursuit of excellence."