Horticulturists are people who understand plants. There is no legal requirement. To be a horticulturist, all you have to do is call yourself a horticulturist. Degreed horticulturalists are plant people with university degrees in horticulture, botany or some other related field. No testing is required to use the term and no continuing education (CEU) is required. Horticulturists are generalists and deal with all sorts of plants. There are no state regulations.
There is also no legal requirement in calling yourself an arborist. To be certified arborists, applicants must have the required number of years in the industry and pass a test, such as in my case provided by the International Society of Arboriculture (ISA). To maintain the certification, a certain number of continuing education hours are required annually and it is enforced. Arborists deal specifically with all aspects of trees. There are no state regulations.
There are two other related categories. First is the Texas Certified Landscape Professional (TCLP) program which certifies people in landscape industry who demonstrate knowledge and skill in horticulture and landscape development. TCNP is similar but specific to the nursery industry. Both programs are run by the Texas Nursery and Landscape Association (TNLA). Annual CEUs are required to maintain certification. On again, there are no state regulations as with architects and landscape architects.
The last category is Master Gardeners. This is a non-professional, amateur, volunteer program that provides free labor to the Texas A&M and other extension systems.
Trees are the easiest of all plants to grow with organic techniques, so make your decision based on which company offers soil improvement recommendations, root flare management, organic fertilization, biological pest control and organic pesticides - but only as a last resort.