Under the Desktop version we were able to charge different clients different prices for the same service (like our #1 client getting preferential pricing). How to do?

Thanks for reaching out to the Community, Januaria55.
 

There's currently a feature in Beta pace called Pricing rules. This allows you to control the price of your products and services. You can offer discounts, or charge different rates for an item/service. You can also charge different rates based on which employee did the work.
 

Since this feature is in Beta pacing, only some subscribers will have access to turn it on. If you're subscribed to a Simple Start or Essentials plan, the feature isn't available in these plans. You might have access to it if you upgrade to a different subscription type.
 

In the event you do have access to use your Pricing rules feature, here's how it works:
 

1. Use the Gear icon, go to Account and settings.
2. Access your Sales tab.
3. In the Products and services section, click Edit.
4. Tick your Turn on price rules Beta option to turn it on.
5. Hit Save, then Done.
6. Use the Gear icon again, go to All Lists, then Price Rules.
7. Press Create a rule or New price rule.
8. Enter any necessary details to finish creating your rule.
9. When you're finished, select Apply, then Save and close.

I've also included a detailed resource about working with price rules which may come in handy moving forward: Set price rules

If there's any additional questions, I'm just a post away. Have a wonderful Tuesday!

@ZackE  RE: You can offer discounts, or charge different rates for an item/service.

Can you do what the OP asked for? Can you set up price levels and assign them to customers so when you invoice a customer the correct price for each item is automatically selected?