Tomatoes and peppers both belong to the Solanaceae, commonly referred to as the nightshade family. While tomato belong to genus Solanum, which includes crops such as potato and eggplant, pepper belongs to the genus Capsicum which includes both sweet and hot peppers. There are various myths and old wives tales regarding the planting of peppers and tomatoes together and perhaps you have had the misfortune to have heard one of them. The fact of the matter is that YES the plants are related and YES they share some common diseases but most people do not have the space in their garden to separate them. The reality is that because the two have similar growth requirements, they can in fact be grown quite successfully together.

Diseases common to both tomato and pepper include Verticillium wilt and bacterial spot. You can limit the likelihood of diseases emerging and spreading simply by following some good gardening practices.

Don’t overcrowd plants. It makes it easier for diseases to spread.
Don’t over or under water. A stressed plant is more susceptible to disease
Don’t water foliage. Wet foliage promotes spread of fungi and bacteria. Instead, water plants at the base.
Avoid working in the garden when plants are wet. Your movements can transfer fungi and bacteria between plants through water splash.

I would advise you to have a look at the disease pages here on PlantVillage to get yourself familiar with things to look out for. You will find a helpful table at the bottom of the plant info pages for both pepper and tomato here:

https://www.plantvillage.com/topics/t...
https://www.plantvillage.com/topics/p...

I have also included some images of the disease symptoms for some of those common to both pepper and tomato

Finally, in addition to diseases, another thing to be careful of when planting is that as tomato plants will likely grow much taller than the pepper you should be careful to position them in a manner that will not result in the peppers being shaded out.