Short answer, it should!
There are thousands of small technical differences between web browsers, the main ones (in no particular order) are:
- Internet Explorer
Even different versions of these feature huge differences!
It’s a constant headache for frontend web developers to get a site to display identically in all browsers, it should be functional and visible to all however.
Does your website work well in all web browsers? Take a look, if not then you could be throwing away visitors and not even know about it. Just because a site works on your phone, doesn’t mean it works as well on everything else.