This is an impossible question, because the "Wild West" was part of the Victorian era. You are visualizing them as entirely separate things because you are used to fiction treating each of these as a highly specific setting with an associated group of tropes. The popular understanding of the Wild West is largely based on folklore and sensationalized fiction, as /u/itsallfolklore has written in a number of answers here, such as Were brothels and prostitution as ubiquitous in the American West as is portrayed in film and fiction? and Why did saloons in the wild west not have front doors but only a pair of small spring-loaded shutters? - it is not more true to life than works of fiction you might see labeled "Victorian" simply because it's dirtier, rougher, and has more (anachronistic!) swearing.

That being said, "Victorian" encompasses such a huge range of stuff in popular culture itself, from refined and witty banter between semi-courting couples in fancy drawing rooms to filthy squalor in London's East End/New York City tenements, that it's hard for me to understand how you can find it so different from the stereotypical Wild West, outside of the obvious geographical issues of the lack of acres given over to cattle back east or the lack of shantytowns on stolen land in England. You might want to take a look at the answers in my flair profile on Victorian culture, of which there are too many to link individually.

Thanks to /u/mimicofmodes for finding the links; we can trust the posts of /u/mimicofmodes to be rock-solid assessments, so I direct your attention there.

The problem with comparing the "Victorian Age" with the "Wild West" is that one is a period and the other is a region, so we begin with trying to compare an apple and an orange. In addition, both are filled with cliché and media treatments that distract from what was really going. The Victorian age describes a period during the last two thirds of the nineteenth century when many styles in clothing, architecture and standards of conduct, aspects of literature, etc., were more or less embraced in the United Kingdom but also in North America, throughout the British Empire and even in other places in Europe. More or less. There was no uniformity, but there was a global marketplace that created converging tastes - more or less!

How this applied to the West - the largest region of North America is another matter, but there were many efforts to adopt Victorian standards of taste and style there as well.

Then there is a matter of what the "Wild West" means. It is, of course, a fiction. If there is any accuracy in the cliché it conjures, that would be described in the first several months of establishing towns, ranches etc., after which, things quickly began looking a lot less "Wild." That aspect of the region suffers from improper generalization, and we must keep in mind that there are "many Wests" as the region's historians are fond of saying. Some places dove right into industrializations; other places saw no need for that sort of technology. Things were complex in such an enormous expanse.

In the midst of all of this, I'm not sure I can agree with the premise of your question - that they seem "like two whole different time periods." Setting aside fictions and unfair stereotypes, one would find a great deal of continuity. More or less.