You have two choices while using alternate munitions (with AC, SRM or LRM).
1. Make a standard weapon attack. This uses the standard S, M or L range damage values on the unit but is noted as using the alternate munition.
2. Make a special weapon attack. This uses the special ability damage (from AC, SRM or LRM) only and uses the alternate munition.
Many of the alternate munitions have different effects depending on this choice. Or some require one or the other.
Swarm LRMs, for example, start as a standard weapon attack, but if you miss, then make a special weapon attack on a nearby unit.
Precision ACs, you choose to make a standard or special weapon attack. If standard, you do the standard S, M or L damage, +1 for the precison ammo. If special, you only use the AC's S, M, or L damage, but you are more likely to hit.