Homeopathy and Herbal Medicine
"Everything is poisonous and everything is medicine - It just depends on the dose"
Homeopathy and Herbal Medicine are each in and of themselves quite different modalities.
Homeopathic medicine was developed by Dr. Samuel Hahnemann. He had been dosing himself with Cinchona Bark (known for containing quinine - used to treat malaria). He observed that it gave him a fever, although it was mild in comparison to the fever and chills experienced by someone who had malaria.
This lead Hahnemann to develop a theory - if he had a patient that had an illness that could be cured by a medicine that when given to a healthy person would produce the same symptoms as the illness (but to a lesser degree). This lead to the phase "like cures like".
Standard medicine practices of this time period where at times barbaric to say the least and sometimes the disease was better than the cure provided. Hahnemann and the homeopathic preparations he made were successful with patients and considered safe, which made it very popular.
Homeopathic preparations (remedies) are made by using a dilution process (usually alcohol is the medium used). They can be of plant, animal or mineral origin. They are diluted to the point that there is nothing of the original raw material left. The potency of the remedy comes from percussing the remedy. The more dilute a remedy the higher the potency.
Homeopathy is unique in that a substance that would normally be considered a poison can be used as medicine such as arsenic (Arsenicum album) or belladonna.
There is debate around the efficacy of homeopathy due to the "lack of substance" to the medicine. However, there has been many historical and clinical cases that show how effective it can be. There are also many scientific studies that have been done that show statistically significant results for homeopathic remedies. Homeopathy can be particularly good for those with sensitive or weak constitutions, for children and animals.
Homeopathic remedies can be obtained by seeing a homeopath for consultation (this can range from 15min to 60mins). From your symptoms they can then dispense which remedies best suit you. This would be termed traditional homeopathy. Alternatively, health stores will stock ranges of remedies that are a combination blend that are for a particular aliment. Remedies can be in liquid form (drops or spray) or they can be taken in a dissolvable lactose based tablet.
In New Zealand you can find qualified registered homeopaths at the NZ Homeopathic Society (https://www.homeopathy.ac.nz/)

Image: NZ Homeopathic Society (2021)
Herbal Medicine has been a form of healing that has been around for 1000s of years. Our ancestors would have found that certain plants when eaten or applied to an sore area helped with healing.
It is the use of plants - whether it be the whole plant or a part of the plant - to heal and balance the body. In more recent years it has been called Phytomedicine or Phytotherapy.
If you lived in countries of Asian decent herbs and plant medicine where used in the form of Traditional Chinese Medicine. If you lived in eastern countries herbs and plants where used in the form of Ayurvedic Medicine for healing. Many indigenous cultures had learnt the knowledge of the plants in their local area and how they could be applied for healing.
Western Medicine could be considered to originate with Hippocrates who worked with his patients in what could be considered a naturopathic way - treating the whole person, not just the symptoms. Hippocrates used herbal remedies in his treatment of his patients.
"First do no harm" - Hippocrates
Herbal infusions where an easy way for the people to utilize herbs. This used a fresh or dried part of the plant (usually the leaves or the flowering top) and they where put with hot water and drank as a tea. If the root or the bark where being used a decoction could be brewed (this took a much longer time to prepare).
The Egyptians had made herbal extracts (tinctures) by using fresh or dried herb and covering them with alcohol for a period of time, then removing the plant material. This left a concentrated form of herbal medicine that would keep for a longer period of time.
Herbs and plant medicine is very versatile in how it can be used. The above methods are still in use today. Along with being able to make herbal wines and vinegars, syrups (these are good for soothing sore throats and coughs), powdered herbs, and salves, ointments and creams for topical use. These are all able to be made with a little study around herbal medicine making in the comfort of your own home.
Herbal Supplementation is now a big business. Herbs have been made into tablet and capsule forms for compliancy and ease of use. Herbal extracts and tinctures are now able to be standardized - this has ensured that a herb is able to be reproduced, has efficacy, within safety standards and is of a high quality. It has also given a surety of active constituents and their percentages within a formula.
Much research has begun to be done on how plants work within the body and their constituents. Many of our medications such as Aspirin from the plant Willow bark (Salix spp.), Digoxin from Foxglove (Digitalis spp.), Quinine from Cinchona bark and Morphine from the Opium poppy. The studies that continue to be done are largely based on specific and singular constituents within herbs. This is not how they have been used traditionally or how they are used by naturopaths and herbalists today. They are used as a whole herb, that has a synergistic blend of phytonutrients working together to help balance the body. Historically and clinically there is much evidence to support the use of herbal medicines. There is more scientific evidence being done, however more studies are needed.
Herbal medicine uses parts from the whole plant. The active phytonutrients can be extracted via many mediums including water, alcohol, glycerin, oils and vinegar. Even though they are natural and a reduced risk of side effects in comparison to allopathic medications, care is still required as for these phytonutrients to be effective they work alongside many of the pathways within our body's, unless of course they are topical applications.

Image: Peter Maselkowski, Unsplash (2021)
So I hope this has been able to clarify the difference between homeopathy and herbal medicine for you. Each can be an affective healing modality.
References
Balch. P. (2006) Prescription for Nutritional Healing, 4th edition; Australia, Penguin
Birch Bark Botanicals (2021), What is a Tincture? Retrieved 18/5/21
Loudon I. (2006), A Brief History of Homeopathy, Vol. 99 Issue 12 Pg 607-610; J R Soc. Med.
Pizzorno. J., Murry. M. (2013) Textbook of Natural Medicine, 4th edition, St Louis Missouri; Elsevier, Churchill Livingstone
WHO (2009), Safety Issues in Preparation of Homeopathic Medicines. Retrieved 16/5/21 https://www.who.int/medicines/areas/traditional/Homeopathy.pdf
Vickers, A. et al (2001) Herbal Medicine. Vol. 175 Issue 2 Pg 125-128; Western Journal of Medicine