So I've been editing in FCPX, making chapter markers in it, exporting a ProRes file, and importing it into DVD Architect to create Blu-rays. I then look at what the timecode is for the chapter markers in FCPX and go into DVD Architect to create the chapter markers, but sometimes the times don't match up. I've noticed when i do a Project and i have Drop Frame selected in Timecode settings, that's when the times don't match up. But when I don't have that selected, the times match up perfectly

What does it mean to create a project with Drop Frame or not with Drop Frame? What is it doing to my final video?

From a visual or quality perspective it has absolutely no effect. DF and NDF is simply a way of labeling each frame but it has no other effect on that frame of video. It is a broadcasting standard for NTSC television. For online delivery it is basically meaningless. The origin of DF began with slowing down the color signal to 29.97 FPS to compensate for real time differences vs. black and white signals in TV sets.

Here's some more general info if you are interested:
The 29.97-second frame rate does not divide into one second as easily as 30 fps does. Since creating a fraction of a frame is impractical, a method of counting and adjusting full frames is necessary. Drop frame timecode counts each video frame. When the remaining .03 second of 29.97 finally adds up to a video frame, it drops a frame number. It does not remove a frame.

Moving the decimal place over from 1.8 frames per minute produces 18 full frames for every 10 minutes. These frame numbers are dropped over time instead of all at once. The distribution of those 18 frames equals about 2 frames (:00 and: 01) a minute, but no frame numbers are dropped in the 10th minute because the process has started over. There are never any frame numbers dropped when the minute is divisible by 10.

This means ten minutes in drop frame 00:10:00:00 is the same as 00:10 minutes in real time. Remember, you are not losing frames. The way they are being counted has been changed. 2,997 full frames are presented every 100 seconds. If you are cutting a scene using drop frame time code, the duration of 60 minutes is exactly 60 minutes and 0 frames. Drop frame is a standard for broadcast networks using NTSC due to this correlation with real time.

Well, it's frames vs fields, so yes, there can be a difference. Transcoding from progressive to interlace is usually not an issue. Transcoding from interlace to progressive can introduce transcode artifacts.

As long as your original media is progressive, the Project is progressive, you should have no quality issues.

To the matter at hand, the project in FCPX and the project in DVD Architect must both be DF or NDF. Mixing the two does in fact mess up timing for things like markers. DF loses roughly a quarter frame or so each second, to the same video in NDF. We run into this all the time with The Louisiana Film Channel when filmmakers don't follow submission specs.