Took me a minute, but if you prefer a tidy/pipy approach, this works also:
library(tidyverse)
col1 <- as.character(expression(Matias, Pepe, Jorge, Elias, Paloma, Paula, Estela))
col2 <- as.character(expression(Paula, Javi, Ulises, Carlos, Pepe, Paco, Pedro))
dframe <- tibble(col1,col2)
dframe
#> # A tibble: 7 x 2
#> col1 col2
#> <chr> <chr>
#> 1 Matias Paula
#> 2 Pepe Javi
#> 3 Jorge Ulises
#> 4 Elias Carlos
#> 5 Paloma Pepe
#> 6 Paula Paco
#> 7 Estela Pedro
dframe %>%
mutate(col1_dupe = !is.na(match(col1, col2))) %>%
mutate(result = if_else(condition = col1_dupe,
true = col1,
false = NA_character_)) %>%
na.omit() %>%
pull(result)
#> [1] "Pepe" "Paula"
Created on 2020-12-21 by the reprex package (v0.3.0)