discrete triangle generator
First, any µA741 based design will not work at 1MHz. You need an op-amp with higher gain-bandwidth product.

The TI design uses a Schmitt trigger to monitor the actual voltage level of the integrator. That's the key feature of that design.

The other design in contrary relies on the pulse-pause ratio of the input square wave. This simpler idea ignores any inital voltage present on the integration capacitor, which would create a random offset you cannot trim away manually. That's why there must be a discharge resistor parallel to the capacitor in that design. That discharge resistor distorts the triangle, unfortunately.