Hey shewt,

Both courses introduce you and teach you in detail the subjects that make up the commerce stream. The eligibility remains same in most of the colleges but nowadays colleges have started demanding maths in bcom programme as well.
B.Com (H) is an undergraduate degree designed to inculcate business acumen in students.You can also pursue courses like Chartered Accountancy along with your B.Com (honors.) Similar to B.Com (H), the difference is that a student can specialize in a certain subject in B.Com (H), which is not possible in B.Com (P). In the latter, a student is given an overview of all the subjects taught in the honors course.
The cut-off for various universities/colleges is relatively higher. Where as for bcom programme the cut-off for various universities/colleges is relatively lower.

The industry demand for the honors program under B.Com is much higher than the regular program.

Hope this helps!