To "make plans" means to plan what you're going to do with someone on a certain day and time. This is the meaning of "plans" with an -s at the end. For example:
Do you have plans for this weekend?
The meaning of this is different from "a plan". "A plan" is an idea for how you're going to do something. Here's an example:
Do you have a plan for what you'll do if you get laid off?
Tell what you're going to do using "plans to ___":
We made plans to meet in a Starbucks at 7:30.
Tell when the plans are using "plans for ___":
I don't have any plans for Thursday. Do you?