I feel like they kinda give off the same vibe. Both are BLs about Fan Culture, the Entertainment Industry, and Social Media.
Both are Celebrity Romance shows but instead of K-pop idols the main character, Han Sekye is a top actress.
Both shows are centered around idols and social media. Just like how Bump Up Business features K-pop group OnlyOneOf, Celebrity also features K-pop idols like Yuqi from (G)I-DLE, Minhyuk from CNBLUE, Junho from 2PM, Hyosung from Secret and Five Girls, Bora from Sistar, and more.
Both are Romance shows about being K-pop idols. Dream High is about 6 students at Kirin Art High School dedicated to becoming Kpop idols. While they learn how to sing, dance, and write songs they start to develop feelings for one another.