Is the chemical formula and structure for phosphorous the same for red and white phosphorous (P4, tetrahedral)? cant seem to find anything specific on google. thanks!

I think red P is a polymeric form of the white allotrope,  but there are also diverse different forms of red, amorphous, tetragonal, cubic, triclinic, and a dark red form.

Aside from the tetrahedral white, there are also cubic, and hexagonal allotropes of white phosphorus.

See

Post 480857

(SHORTY: "Allotropes of Phosphorus", Stimulants)