Were there ideological differences between Presidents George H.W. Bush and George W. Bush?

There is a surprising amount of consistency and similarity between the two Bush presidencies. George H.W. Bush took over as president in 1988, and had to deal with financial deficits from the previous regime, as well as a slew of foreign policy issues.
Similarly, George W. Bush took over and dealt with lingering budgetary concerns from the previous electorate and was still entangled with some of the exact same foreign policy issues that cropped up during his father's presidency. Both of the presidents took a stance of reducing the budgetary deficits, increasing military might and wielding it to curb foreign threats, and they also both shared ideologies regarding education in America and attempts to improve it overall.
The foreign conflict that would become Operation Desert Storm arose during Bush Sr's time in office, and eventually a second desert storm happened with the War on Terror in the early 2000s under Bush Jr. Both presidents sent a large military force to deal with militant extremists as well as to prevent middle eastern terror organizations from seizing control of oil reserves, which would give them extra political might in their territory.
Additionally, both presidents introduced legislation to improve education. Bush Sr. implemented the Education Excellence Act and Bush Jr enacted No Child Left Behind. One of the major points of difference in their presidencies was taxation. While neither of them wanted to raise taxes (a typical platform for Conservative Republican politicians), Bush Sr. had little choice but to enact sweeping tax hikes in conjunction with the predominately liberal congress to reduce the deficits incurred under the previous president's term.