They are different and you need to setup 301s to correct, also check all your menus etc to make sure that you use them consistently - this includes in emails etc - consistency is the key.
You can go with slashes or no slashes, as long as you are consistent, I have run sites both ways.
I will disagree with Jesse one thing - I would strongly recommend using the ending slash. I have several reasons why.
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The url ending in a slash traditionally represents a folder with pages/documents/images inside that folder. Used to be that we would use a URL like /folder/index.htm with index.htm being the default page. It used to be that if you did not designate any file as an index file, assuming the permissions on the folder were set correctly, you would see all the content in that folder. Later, you could designate a default index file and so when you left it blank by ending in a slash it would show the content of the default page without needing the index.htm to be included. Now this issue can cause duplicate content problems (but that is another story).
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Knowing all that above, many of your web analytic and other reporting software would create reports using a given folder Google Analytics is a good one. If you use the conent drilldown tool, it automatically organizes your reports by looking at the slashes and then grouping pageviews and visits according to the folder structure.
3) Separately, you had development code that used the folder system in the url as a way to parse what the user wants and then deliver a page. This is why you can now have a url like /article/file and you do not need a .htm or .php or .html at the end as the server knows what to do with it without seeing the final extensions.
What happens then is that you end up with URLs like this
/toys/age6-8
/toys/age6-8/redball
/toys/age6-8/blueball
/toys/age9-10
/toys/age9-10/remote-car
/toys/age9-10/remote-control-train
You can see this is a toy store and they are grouping toys by age. Balls are better for younger children vs remote vehicles for older children. In your GA reporting, if you assume that a slash indicates a new folder
/toys/age6-8 would not be included in the report with the products as it would be seen as a page within the /toys/ folder. Same thing with /toys/age9-10
You have your most important page not grouped with all the products it contains.
This is one of the reasons that I prefer ending with the slash. Can you do it the other way, sure, but it just adds more hassle. The folder ending in a slash is a convention that most people follow and frankly, you will find that users also tend to end in a slash when they put in a url. You end up with links to your site where they have a slash and one is needed.
Old habits are hard to break and so this is why I recommend going with the ending slash.