Shelling Barrier, Spell Barrier, Self-D Barrier, Strat Barrier and Barrier, are all entirely different things.
Shelling Barrier reduces damage from start of battle skills (Shelling skills) by a percentage, for the entire division. If a unit has 40 Shelling Barrier, they reduce that damage by 40%. This doesn't block Poison Blast/Field/M-Field.
Spell Barrier does a similar thing, only for end of turn skills like Fire Blast, Light Field etc. Same percentage gimmick, same weakness to Poison Shelling/Field/M-Field.
Self-D Barrier is for self-destruct skills. Strat Barrier is for tactical skills, though keep in mind that it doesn't block any debuffs they give, just the damage.
All of the above skills stack multiplicatively if they're on different units, so the goal is usually to have the value of 100 on a single unit if at all possible. Which ones you need depend on what you're facing, what difficulty you're on, and the set-up of your division.
Barrier is the only skill that provides a value for the Barrier number, which acts like an extra pile of HP for your entire battalion. Barrier values stack directly for the entire battalion. So the more you have, the more effective it is in theory. At lower difficulties, enough of it can act as a replacement for Shelling Barrier, or work with lower values of it to prevent start of battle damage to your divisions. It also works takes the hit for Poison skills, which can make it surprisingly useful in some niche scenarios... though it's hard to build for it.
Lastly, I don't know if it's intended or a bug, but usually, Barrier from Tactical Skills overrides the Barrier from the Barrier skill, so if the latter is higher, don't use any Tactical Skills that give Barrier before it's actually lower, or you're effective wasting it.
