No.
“SaaS” has, like “Cloud”, become a term that no longer really reflects its current meaning. Time marches on and while “SaaS” used to be a term that differentiated web software from downloaded or on-prem business software, that on-prem/download world has shrunk almost to irrelevance. Thus, the term’s meaning has marched on with time.
Of course Facebook, Twitter, etc. are software-as-a-service, provided over the internet.
But the definition / line for “SaaS” is applications whose business model is primarily a subscription fee for software.
Similarly, ecommerce companies are generally not “SaaS”. They do have primarily a subscription model (unlike Facebook or Twitter) but the fee is for physical goods.
There are companies a bit in the middle that may feel consumer-y like Slack, but while the free version of Slack has incredible traction, Slack’s business model is clearly in its ARR and the fees its charges for the paid versions.
