Check The popups the see what the marker and the circle actually depicts.

library(leaflet)
m <- leaflet() %>%
     addTiles() %>%
     addMarkers(lat = 23.00596984, lng = 72.601229, popup = "Kankaria Lake, Ahmedabad (A popular Tourists Spot Near my house") %>%
     addCircleMarkers(weight = 10, lat = 23.00579494, lng = 72.60467117, radius = 50, popup = "Area in which I live") 

m