why are strong bases only stabilised by H+ ions while the moderate one,s just attack any +ve charge

Dear student
I guess you have confused yourself between nucleophilicity v/s basicity.
Nucleophilicity and basicity arevery similar propertiesin that species that are nucleophiles are usually also bases (e.g.HO-, RO-) or you can say thatbasicity is asubsetof nucleophilicity.
All nucleophiles are Lewis bases since they donate a lone pair of electrons. A “base” (or, “Brønsted base”) is just the name we give to a nucleophile when it’s forming a bond to a proton (H+).
Nucleophile attacks any positive centre other than hydrogen (H⁺).