On my garmin 305 edge a route shows a distance of
5.1 miles
on Strava I get 6.1

it is a timed lap that is on a mix of bridleway/fireroad and then off under trees on a path, used regularly in the forest.

Done this a few times say 15 or more including running, and altered the setting to show,
so who should I believe?

Try looking at the routes from both in one of the online mapping programs that allows you to view satellite images. When I was having the same problem I found that the Strava trace was much closer to the paths on the image than the Garmin which seemed to straight line corners. Even with the Garmin set to it’s most accurate settings Strava was still better. I only use my Garmin for route following now, it is quite an old Oregon series one though so I don’t know if the modern ones are more accurate.

My Oregon 600 has options for how often and on what basis to record track points. That affects short/twisty routes a lot.

You should believe the longer one. Then it makes your times seem better.

By Strava do you mean your mobile phone?

The Garmin ought to be more accurate, surely? I know mine is much better than my mobile at picking up segments etc.

Sorry no it after uploading into strava I get more than on garmin as a unit and on garmin connect.

Check whether the times match on Garmin / Strava, including the moving time / paused times.
If you are not going very fast, the Garmin might autopause. So it won’t count that as the distance, but Strava will.
Best to turn off any auto pause options.

They use different map data.

Auto pause can confuse Strava and they work out the stopped time anyway, and perhaps a little more accurately as a Garmin that’s working off GPS alone can be tricked into unpausing if the GPS drifts when standing around, which is common, or might not unpause if you’re going below the threshold speed.

However, if you are using a speed sensor on the Garmin, then it’s a lot more accurate but will be quite different to Strava and also to most people using Strava who mainly use their phones. Speed sensor will be tracking the actual ground rolled.

When uploaded to Strava they will adjust using topographical satellite data so it will differ from the Garmin or Connect. Again, if you use a speed sensor it might prefer that to the corrected data, though not sure if they do that. I know they favour the barometer in a Garmin over their own altitude data.