Without modules

Your code in ui might look like this:

# ui.R
# ...
numericInput("sample_ratio", ...),
plotOutput("mtcars"),
downloadButton("mtcars_download"),
plotOutput("iris"),
downloadButton("iris_download"),

and your code in server might look like this:

# server.R
# ...
output$mtcars <- renderPlot({
    ...
})
output$mtcars_download <- downloadHandler({
    ...
})
output$iris <- renderPlot({
    ...
})
output$iris_download <- downloadHandler({
    ...
})

The different plots hold the relevant parts but you have to duplicate the download parts although they are the same. Moreover if you decide to add an option not only to download the plot but also the data you have to add the code to every plot.

With modules

You can focus on the fundamentally different parts, moreover your code is less error-prone (e.g accidentally download the same plot from two different buttons.) You also do not have to worry about having to give a different name to every one of your download buttons.

# ui.R
plotDownloadUI("mtcars"),
plotDownloadUI("iris")
# server.R
...
callModule(plotDownload, "mtcars", plotMtcarsReactive)
callModule(plotDownload, "iris", plotIrisReactive)

plotDownloadUI <- function(id, height = 400) {
    ns <- NS(id)
    tagList(
        fluidRow(
            plotOutput(ns('plot'), height = height)
        ),
        fluidRow(
            column(
                2, offset = 10,
                downloadButton(ns("download_plot"), "Download figure")
            )
        )
    )
}

plotDownload <- function(input, output, session, plotFun) {
    output$plot <- renderPlot({
        plotFun()
    })
    
    output$download_plot <- downloadHandler(
        filename = function() {
            "plot.png"
        },
        content = function(file) {
            ggsave(file, plotFun(), width = 16, height = 10.4)
        }
    )
}

The whole code is available here and you can see the working app here.