library(tidyverse)

df <- read_table("type_1    type_2
fire    leaf
leaf    fire")

df %>% 
  pivot_longer(everything()) %>% 
  count(name, value) %>% 
  pivot_wider(names_from = value, values_from = n)

# A tibble: 2 × 3
  name    fire  leaf
  <chr>  <int> <int>
1 type_1     1     1
2 type_2     1     1

df %>% 
  select(-name) # If you don't want the name column