Yes.

They are both basically the same but with some subtle differences. Think of "spare time" as "leisure time" and think of "free time" as "availability". So if you want to know if someone is available to meet with you tomorrow you would ask "Are you free tomorrow in the afternoon? Do you have any free time to talk to me?". But if you want to know what people do for leisure (sports, reading, movies), you would ask "What do you do in your spare time?"

They are synonyms, but we use them in different situations in English. For example: If you were asking someone about their hobbies, or what they do in their "spare" time, you would use spare. Free time is used more when it's referring to a break in between something, like a free class period between lessons.