No worries. I agree "SaaS" might be a bit of a misnomer in our case, but we wanted to distinguish ourselves from desktop software (which still rules our industry).
Hi, other founder here. Does "SaaS" have to be synonymous with a subscription business model?
I wouldn't put it synonymous, but most of the SaaS products I've ever paid and used were based on monthly/yearly subscriptions and were not "pay per use", so that's probably why people mostly use it that way - but there's credit token models though, e.g. SauceLabs or Audible where your monthly payments grants you N tokens to spend now or later.
SaaS does not imply a recurring billing model. Stripe, Twilio, Square, Facebook, Google - all SaaS, none have a recurring billing model.