There are differences and they are far from mythical!
A big one: Liquidity. If you spend $100,000 today, you all of a sudden have a $100,000 less in your bank account. That may limit what you and your team can do this year - because budgets are finite. If you have the option to pay $20,000 each year over 5 years your liquidity goes down by that amount each year. Much easier to plan and usually less risky.
Another one: Flexiblity. If you don't need the product or service after year 3 any more, stop it. You paid $60,000 instead of $100,000. Less. Money. Spent. (And yes, it also goes into the other direction (pay more than $100,000 if you use it longer) but that's a trade off many businesses are willing to make. 5 years is a long time, things change.)
Last but not least: Opportunity costs. Paying $100,000 at once is expensive because it means you can't invest the money into something else that generates interest. If you pay $20,000 each year it means, that you still have $80,000 in the first year, $60,000 in the second and so on. Use this remaining money to invest it into something that creates interest for you (bank account, stocks, index fund, ...). That's another win! (And also the reason why big companies pay their bills as late as possible - it adds up for them!)