If you booked with two different airlines then yes, you will have to clear customs at BKK, claim your baggage and then go through the boarding procedures for the second flight.
Did you book the flights yourself or did you use an agent? The only info on your profile is that you reside in the UK...so you don't need a visa for a short stay for Thailand.
Here is a link to the official BKK website.
http://www.suvarnabhumiairport.com/en/landings/passenger
And you'll see info on what to do with/without a boarding pass.
Since BKK has a huge, really huge terminal I'd suggest looking at where you'd arrive, where you'll clear customs and then where you'll go through boarding for the second flight. Here's a link to the map:
http://www.suvarnabhumiairport.com/en/124-within-the-terminal
And so we come to Bangkok Airways who have this helpful page:
http://www.bangkokair.com/pages/view/web-check-in
This is important as it has to do with how much time you'll need to plan on between arrival and departure:
"Web Check-in is available from 24 hours up to 2 hours prior to departure time.
Important note: Passengers on international flights who have completed web check-in are required to present themselves at Check-in Counter at least 90 minutes prior to departure time to obtain a boarding pass and verification of travel documents needed for Immigration and Security clearance."
Yep, 90 minutes. So your proposed flight to Samui isn't going to work...
and you haven't taken into account any possible delays on the Emirates flight. They're a great airline but no one can guarantee there won't be delays due to weather, etc.
AND...further down the page, there's a nice flow chart and it says the baggage has to be checked 2 HOURS before departure.
and since you'll be doing the reverse on your trip home, plan ahead now and check out what you'll need to do then...
One more thing (from another site):
"Transfer Lounges - Free lounges for the purpose of resting in between flights. Equipped with reclining leather chairs. Location: Airside, Concourse B and D (west side)"
Those who have used this airport will no doubt have their personal suggestions and experiences but this will get you started with all the official info.
Travel well and return happy....good luck