I agree with Jaspar that your first paragraph is prompting for an essay, but is your second paragraph asking for examples, meaning references that discuss the difference?

Here are three:

1. Richard Skemp's article on Relational Understanding and Instrumental Understanding.

2. The five strands of mathematical proficiency described in Adding It Up. The first two strands are conceptual understanding and procedural fluency.

3. Phil Daro's 10-minute video on Four Levels of Learning.

I agree with Jasper that your first paragraph is prompting for an essay, but is your second paragraph asking for examples, meaning references that discuss the difference?

Here are three:

1. Richard Skemp's article on Relational Understanding and Instrumental Understanding.

2. The five strands of mathematical proficiency described in Adding It Up. The first two strands are conceptual understanding and procedural fluency.

3. Phil Daro's 10-minute video on Four Levels of Learning.