Joe Shmoe off the street has no clue about the diseases processes, treatments, anatomy and physiology of the patients, or the medical reasons behind why technical skills are applied. There is a HUGE difference between someone with no degree and someone with a degree.
I am very passionate about this issue because I went to school to learn all I could, and someone who has not taken the time or expended the effort should not be held in the same regard as I am.
At most vet clinics, reputable ones at least, you will be held in higher esteem if you have a degree and a license, and will likely be paid more.
Some places, and rightly so, even differentiate between the duties an assistant and a technician can perform.
If you're really interested in working with animals, I would encourage you to pursue a degree! I would hesitate, however, to take any portion of it online - it's a difficult program. Mine was accelerated, and I graduated in 16 months.
And yes, you must take the Veterinary Technician National Examination, and in some states, take a practical and/or jurisprudence exam, to receive your license. You can be called an LVT, RVT... depending on what state you are in. They are all the same.
You must maintain your license with continuing education for the rest of your career.