What is the difference between routine and schedule? Are these words adjectives?
Routine is usually used as an adjective or a noun.
Schedule is most often used as a noun or verb.
Schedules are planned out and often written down. Routines can be activities that are done without planning, things that you are used to doing on a regular basis. Many people might do the same things every morning in the same order, but that's not necessarily something they scheduled for themselves.
Routine is like a habit. It is something you don't need to write down because you've done it so many times over. Schedules can be things that are only followed for a certain day (special schedules for certain times).
Schedule cannot be used as an adjective. Routine can.
It has become routine for me to work out in the morning. You cannot replace routine with schedule.
Schedule can be used as a verb. Routine can, but the occurrences are rare.
I scheduled a meeting. (You wouldn't say I routined a meeting. That's not something you do often.)
Both can be used as nouns, but they cannot always be used interchangeably.
I followed my schedule for the day. This sentence indicates that you designed/outlined a schedule and followed it for that day.
I followed my routine for the day. This sentence indicates that you did your normal activities for the day.
So no, I would not say that schedule and routine are synonyms.