So, the pause is only to ensure the medical community has a plan to address these ultra-rare incidents should they occur.
Sounds like they're pretty isolated to Women under 50 btw, which leads to the demographic of those taking birth control pills which have known clotting side effects. It's more likely the pill is the cause than the vaccine.
There were also blood clot scares early on with either the Moderna or Pfizer, I believe, that eventually turned out to be so statistically insignificant that they moved on.
Actually it's the AstraZeneca vaccine that's been associated with clotting in Europe and Canada. This vaccine is not being distributed in the US, but is being manufactured here.
There was an anaphylactic reaction associated with both Pfizer and Moderna that was investigated after a few cases, but yes, was statistically insignificant... as this clotting issue also appears to be.
20% chance of clotting with COVID, less than 1% with the J&J vaccine.