Down time is when something is not available or not working, for example a website goes down. Spare time is free time that someone has when not working, when he or she can choose what they want to do.

Well, the Merriam-Webster dictionary (US site) has this definition. Definition of downtime 1 : time during which production is stopped especially during setup for an operation or when making repairs. 2 : inactive time (such as time between periods of work). "napping during our downtime"; "an injured athlete facing months of downtime". So both of the above responders seem to be (partially) correct about "downtime". At Collinsdictionary.com (UK site) it lists the #2 sense as "mainly US", which might explain the different thoughts. https://www.collinsdictionary.com/dictionary/english/downtime