According to Toby Fox, Deltarune (2018) is completely unrelated to the hit game Undertale (2015).
At the start of Deltarune chapter 2 when you examine the computer in your bedroom the description talks about how the final boss of a game on there has rainbow wings. This is a reference to Asriel Dremurr's final form in Undertale.
"Don't forget" "Beginning" "Friendship" and "Field of Hopes and Dreams" all share the similar song, but instrumented differently.