Does it take the same wait time to get a refund when filing taxes myself by mail and by using a tax preparation service (USA)?

It depends on what you count as "shipping time".

If you're filing by mail, you obviously have to wait for your return to physically arrive at the IRS. Then you have to wait for someone at the IRS to open the envelope, scan the physical return into their system, and for their system to process it (and potentially to flag something that a human needs to look at because it didn't recognize something you entered). Depending on when you file your return, this can take a while and that may or may not be what you consider "shipping time".

If you file electronically, you should get your refund just as quickly as if a tax preparation service electronically filed for you. Electronic filing is generally preferred since it skips all the manual processing steps.

There are several things that affect how long it takes to get your tax refund.

First, there is the time it takes for the IRS to process your return. The IRS is able to process tax returns that were submitted electronically (e-File) quicker than returns that were submitted by mail. It doesn't matter if you do your taxes yourself or pay someone else to generate the return; what matters is if it was e-filed or mailed.

Next, there is the time it takes to send the refund. With your federal return, you have the option of receiving your refund by direct deposit instead of a paper check. The direct deposit option is faster than if they need to mail you a paper check.

There are some things that can delay the processing and payment of your return/refund. Certain credits or inconsistencies may trigger an additional review of your return before the refund is paid. For these, it won't matter whether you completed your return yourself or had someone else do it, and these IRS reviews are not predictable.

Finally, the IRS is still experiencing a backlog due to the pandemic restrictions, meaning that it may take longer to receive your refund than it did in previous years.

The IRS says that 9 out of 10 people who file electronically and participate in direct deposit receive their refund within 21 days of submitting their return.