Is an undergraduate in engineering a professional degree or an undergrad degree?

In the chart linked by mmcwilliams, an undergraduate degree in engineering would normally be a "Bachelor's Degree" - assuming the certificate awarded at the end says "bachelor of science" or something similar.

The differentiation here is usually that a professional degree follows a bachelors or undergrad degree. Law school and medical school are categorized differently than masters degree programs. In US colleges an engineering degree would typically be an MA and in some fields the MA is not a terminal degree.

This varies a lot.

Some engineering programs make sure students are learning specialized practical skills, others make sure they get a solid grounding in basics so they have an easier time in picking whatever engineering discipline strikes their fancy.

There are pros and cons for both.