I ask because if you look at a tomato, the way it grows on a vine, its color, the texture, and make up of its skin and internal structure it seems very much like a pepper. The only thing I can think it lacks that a pepper has is any amount of spice. I wouldn't be surprised to learn that it has trace amounts of capsaicin.
There are different unrelated plants called "pepper" in English. Black pepper (species of the Piper genus), as indicated by Chris, is not related to tomato and doesn't "look alike".
I guess the OP meant actually a different plant (Capsicum genus), to which the common bell pepper (Capsicum annuum) belongs. This one is similar to tomato and they both belong to Solanaceae, the same subfamily Solanoideae, but different tribes: tomato is classified in Solaneae and Capsicum in Capsiceae.
In this study you can see, how distant phylogenetically the two genera are. Currently accepted classification generally reflects phylogeny, and there are three more tribes that are closer to Capsiceae, to which Solaneae is nevertheless a close relative.
The most striking morphological difference between Capsicum and Solanum is that the first one is characterized by hollow fruits, while tomato and other Solanum species have fleshy berry-like fruits.
EDIT: It's actually not a difficult task for one's imagination to see that the two types of fruit are structurally very similar. In reality a pepper-structured tomato cultivar is known, and even quantitative trait loci underlying this morphological trait were already found.
They are not related, both plants belong to different taxonomic orders:
Pepper belongs to:
Tomatoes belong to the
If you look at Capsicum (as MattDmo suggested) then this is different. These peppers belong to the same order (solanales) and family (solanaceae) as tomatoes. They form a different tribe (Capsiceae).
Wikipedia states on this: