What type of visa should I apply for if I'm traveling from Canada to Thailand for an extended trip including Laos and Vietnam?

Each time you arrive you will receive a new visa exempt 45 days, except for the last time when you will receive 30 days. No need to apply for any of these. You will be stamped in on arrival. Just make sure you are able to show evidence of leaving Thailand each time in case they ask.

𝗧𝗵𝗶𝘀 𝘄𝗶𝗹𝗹 𝗽𝘂𝘁 𝗺𝗲 𝗼𝘂𝘁𝘀𝗶𝗱𝗲 𝗼𝗳 𝟰𝟱 𝗱𝗮𝘆𝘀 <- I don't understand what that means.

Right now the 45 day visa exempt entry program for 52 countries runs until Mar 31st

So when you arrive the first time you'll get stamped in for 45 days <- that stamp will cancel when you stamp OUT of the country at the Lao border.

Then when you fly back in and re-enter the country from Vietnam IF it's before Mar 31 you will get a NEW 45 day visa exempt entry and you can extend that one time by 30 more days if you need to at the immigration office where you stay for 1900baht