Are black and pink algae the same thing?

No, and treating them the same way will waste your time. Black algae is a cyanobacteria that digs roots into plaster or concrete, requiring a stainless steel brush and heavy shocking. Pink algae is bacteria (usually Serratia marcescens) that grows as slime and needs scrubbing, shocking, filter cleaning, and checking circulation. Consistent chlorine levels are your best defense against both.