There is much confusion between the term "braided rein" and "laced rein". I will try and clarify the two types so that you can more effectively understand the construction of the two reins. This will help when you order new reins or a bridle so that you will receive exactly what you want.
Laced reins come in a variety of widths. 3/8", 1/2" and wider. Laced reins have holes punched all they way down the center of the rein. The holes have a long strand of leather that is laced side to side forming a herringbone pattern down the entire hand held part of the rein. This rein offers a lot of grip and can be easily held as it is not very thick or wide. Laced reins are very common on double bridles as the snaffle.
Braided reins also come in a variety of widths. Mostly 1/2" and 5/8" as anything wider usually becomes too thick to hold in your hand. Braided reins are made from long strands of leather 3 or 5 strands that are braided or plaited together for the entire hand part of the rein.
I hope this helps you clarify the difference between and laced and braided reins.
Have fun and be safe,