No, they're different because they have different models.
I checked them on custom battle and they're not related.
Here's what it says for me.
mercenary_barracks3 requires factions { byzantium, }
{
capability
{
recruit_pool "Skythikoi" 1 0.25 2 0 requires factions { byzantium, }
recruit_pool "English Huscarls" 1 0.16 2 1 requires factions { byzantium, } and not event_counter HEAVY_MAIL_ARMOR 1
recruit_pool "Alamanoi" 1 0.12 1 0 requires factions { byzantium, } and event_counter HEAVY_MAIL_ARMOR 1
recruit_pool "Latinikon" 1 0.16 1 0 requires factions { byzantium, }
law_bonus bonus -4
law_bonus bonus 1 requires event_counter is_the_ai 3 and not event_counter is_the_ai 4
law_bonus bonus 2 requires event_counter is_the_ai 4
}
material stone
construction 12
cost 6000
settlement_min large_city