You are wrong to assume that 1 grid cell (pixel) side is 1 meter in UTM or any other coordinate reference system. It can be anything (up to ~600 km for a single column raster, if you want to stay within UTM zone boundaries).
It is also important to note that cell size is not constant. With a longitude/latitude coordinate reference system (CRS), I assume that is what you erroneously refer to with
WGS84, it changes with latitude. With a planar CRS cell size may change (decrease) as you move away from the origin of the CRS (unless you are using an equal-area CRS; UTM is not equal-area); there is an illustration here). For a very small area as in your example this variation is minimal.
The area covered by a raster should be very similar to that of a vector representation, except for the extreme case where the island is reduced to only a few grid cells.
Here is some R code to illustrate this for the Isle of Man, for vector data (lon/lat and UTM) and raster data with 30 arc-seconds, 10 m and 1 km spatial resolution (length of the side of each cell).
g <- getData("GADM", country="Isle of Man", level=0)
g <- vect(g)
#  "+proj=longlat +datum=WGS84 +no_defs"
# rasterize the vector data to a lon/lat raster
# with a 1/120=30 seconds spatial resolution (a bit less than 1 km2)
r0 <- rast(g, res=1/120)
r0 <- rasterize(g, r0)
Transform the vector data to UTM (but staying with the WGS84 datum) and rasterize again.
gutm <- project(g, "+proj=utm +zone=30 +datum=WGS84")
#  "+proj=utm +zone=30 +datum=WGS84 +units=m +no_defs"
# 10 m resolution
r1 <- rast(gutm, res=10)
# 10 10
r1 <- rasterize(gutm, r1)
# 1 km resolution
r2 <- rast(gutm, res=1000)
r2 <- rasterize(gutm, r2)
Now compute the size of the island for the different representations.
area_lonlat <- area(g)
area_utm <- area(gutm)
area_rst_lonlat_1km <- area(r0)
area_rst_utm_10m <- area(r1)
area_rst_utm_1km <- area(r2)
akm2 <- cbind(area_lonlat, area_utm, area_rst_lonlat_1km,
area_rst_utm_10m, area_rst_utm_1km) / 1000000
area_lonlat area_utm area_rst_lonlat_1km area_rst_utm_10m area_rst_utm_1km
[1,] 579.67 579.35 579.72 579.36 579
Above are the five estimates of the island size in km2. There is some minor variation, but less than what you report. With the 10 m resolution it is only 0.07 km2 compared to the polygon.
Relative to the size of your island, 0.8 km2 is a lot, so you may need to use a higher spatial resolution. (It depends on what you ultimate goal is, presumably that is not to estimate the island size).
Based on your description I am assuming you used the wrong spatial resolution. There are other possibilities: the raster data can be of poor quality, the other source can be wrong. But you do not provide much to go on; you do not mention the island's name, nor how you calculated its size.