The cross planks at the top of your trestle table legs would classify as cleats.
A common table has an apron and the end boards that run perpendicular to the board grain direction become the cleats. A cleat could be the board cross joining a solid wood door where they hold the boards together and keep the door flat. If the boards are separate(not glued together) , cracks will form between the board as they dry. If they are glued together , then there must be allowances for dimension change or there will be splitting etc.
A solid 30 inch wide tabletop moves quite a bit (1/4-1/2 and inch) over the seasonal change in humidity. Therefore the cross boards or cleats need to be attached in one of many ways that allow wood movement but still hold the tabletop firm and flat.
The simplest way is screwing the top thru the cleat in the middle and at the sides of the top. The side holes need to be slots in the direction of movement to allow for movement. There are special elongated washers available called expansion washers that facilitate the movement.
. ( This should ling to lee valley under expansion washers.)
Other ways are buttons screwed in the top and indexed in a slot in the cleat or s clips that do the same.
this should show the s clips in use.
I hope this helps woodworking if fun and useful. Understanding wood properties is vital to quality design. Designing for wood expanding and contracting if one of the ots important factors. It often starts with the best choice of wood for the project.
As mentioned above , construction lumber is best used for projects that will be fastened together firmly using wood construction techniques. Avoid tight circles/growth rings in the end of boards in furniture other than narrow pieces.