There has been a lot learned since the time when NY had it's spike. This has lead to better outcomes in many cases, however this can still be a really devastating illness.
If you're interested, look up "medcram" on YouTube. Along with information I've received from my day job, this has been really informative. Where I am, the new cases have fallen to zero, however there are still a handful of very sick people in our health system.
Even in the beginning, deaths lagged infections by a couple of weeks, and with better knowledge, the lag may now be greater.
What you should really be alarmed about is the positive rate of tests. The idea of widespread testing is that you can spot places with outbreaks early, and deal with them. Another state in Australia that is having a second wave is shutting down apartment blocks and maybe suburbs rather than the entire state. Other states have blocked movement between that state and theirs.
This more localized shutting down is possible because the overall positive rate is low (in our state, for the general public, it peaked at well under 1%). And we remained significantly shut down for 2 months.
In the US, the recommendation is to halt reopening if the positive rate exceeds 5% (which is still a really scary high number). However you are seeing positive rates exceeding 20% with little consideration (apparently) of reversing or even slowing the reopening process.
Many of the newer cases in Florida (and this is not limited to Florida) were initially younger people, primarily because these were the people more likely to go to the types of reopened entertainment venues that have the most crowded conditions. It may also be because older and more compromised people tended to take more precautions.
The death rate from COVID-19 is lower in younger people, however I have heard that more older patients are now presenting in Florida. I'm not sure how reliable this is, however it is certain that health workers in Florida are suffering increased infection rates (similarly to what happened in NY).
In contrast to @shrtrnd
I don't think that the reporting coming out of the US is particularly sensationalist (but I'm only seeing stuff from CNN and MSNBC, etc). However, I do agree with his advice regarding hygiene and keeping the more vulnerable safe.
One of my friends was tasked with setting up the COVID clinics in my state. She related to me about the stress for people in the front line, and as the person also responsible for dealing with consumable PPE also needed to deal with dwindling supplies. My state never ran out of PPE, however some disposable PPE that could be cleaned (e.g. face shields) were cleaned and reused.
To get an idea of what it was like, when she went into the clinic area, she would first remove her clothes and don scrubs, then she would go into a sterile area where she would put on masks, gloves, goggles, face shields, and neck to knee, long sleeved disposable outer wear. If she needed to go to the toilet, the entire process was reversed, and then repeated. She went through at least 5 full sets of this every day (excluding up to three changes of gloves for each patient, and additional mask changes if they became damp). She also now has a couple of scars on her face where the mass were rubbing.
This is exactly what health care workers would be doing (if they could) in the US. The fact that some single use masks are being reused for days (even discounting the reports of weeks) is clearly an issue.
Unfortunately, the US is currently grouped with Russia and Brazil (and maybe India). Even the UK, recently seen as a basket case, has pulled itself together.