Reproduction numbers
First of all, the basic reproduction number ($R_0$) refers to the contageous person meeting susceptible people only: the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. So $R_0$ is not affected by vaccination status (or acquired immunity) of the population, but it includes factors such as being contageous already during incubation period (i.e. while still free of symptoms, how contageous a single virus particle is, how long a virus particle lasts under "normal" circumstances, ...)
In contrast, the effective reproduction number R includes the effects of vaccination, acquired immunity, behaviour and other measures to reduce infection risk.
The wiki page linked above lists $R_0$ for Covid-19 as 1.4–3.9 and for the Spanish flu of 1918 as 2–3.
Now, for the countries that still have just a few Covid-19 cases and that are just beginning to take measures to slow the spread, the effective reproduction number will be roughly the same as the basic reproduction number: noone is immune yet, and no measures to reduce the number of contacts yet.
Does that mean that the flu actually has a much higher transmission rate in un-vaccinated people and the average works out to a number similar to Covid19 in an unvaccinated population?
Sort-of, but rather the other way round: it means that the effective reproduction number is lower for the flu even though their $R_0$s are similar.
This review paper gives an R of about 1.8 for the 1918 flu and about 1.3 for the "normal" seasonal flu.
Vaccination
Or does in mean that vaccine doesn't stop the spread as much as it really stops the disease?
That can also happen. Of course, the best and intended outcome of vaccination is that the acquired immunity is sufficient to prevent infection. Which means that the vaccinated person cannot spread the disease. However, not all vaccinatione we have and use achieve this - we still use them if they greatly reduce the severity of the disease. E.g. even with varicella vaccination 10 - 30 % of the exposed to get chickenpox (but even with them, serious disease is avoided).
For the flu, the difficulty is that new strains appear regularly. This is also the reason why flu vaccination is done annually with a newly developed vaccine while e.g. for MMRV, pertussis, polio boosting with the existing vaccine every 10 years is sufficient (immunity actually may last even longer, up to lifelong*, but that varies by person, and since many vaccines haven't been around that long, we don't know for which that is the case). In fact, flu strains appear so often that the development of the annual flu vaccine includes educated guesses which strains are going to be important for next season. Sometimes that guess is off. Wikipedia on flu vaccination has a table giving effectiveness (actual reduction of infection risk) between 10 - 60 % for different years.
Even if the acquired immunity by vaccination is for the wrong strain, one may still benefit from cross-immunity(?) in that the disease will be milder and possibly shorter.
* also acquired immunity after a disesase does not always last life-long, e.g. a pertussis infection will achieve immunity for 4 - 20 years only (4 - 12 years for vaccination)
