What

准时： on time ( to emphasis on the physical aspect of being on time)
我每次见朋友都会准时到。

按时： on time ( for event or action take place strictly following a scheduled time )
生病了，一定要按时吃药。

按时 就是没有晚、及时的意思。
比如你踩着铃声进班、踩着点进教室不算迟到，赶上了的意思。in time

准时就是一分都不差、不多也不少。是几点就是几点。不慌不忙的感觉on time

如果老师要求你准时到班，但你踩着点进教室，只要铃声响了，不好意思算作迟到的感觉。

准时 "punctual" 准时 can be used as adverb or adjective
不管是刮风下雨，小明总是准时去上学。Whatever happens, Xiao Ming is punctual to go to school.

按时 "on time or to follow the specified time" 按时 can be used as adverb
老师再三强调学生应该按时完成作业。 The teacher reminds her students to hand in their homework on time.