What is the different between a Celeron and a Pentium processor or an AMD for that matter?

Honestly, Vic, unless you are planning on mining BitCoin, solving quantam equations, doing speed trading where microseconds count and latency = ruin, or doing HARDCORE gaming where, again, lag means "death," any moderate to good processor will do.

The processor CAN make a difference in latency / lag, especially if you have a lot going on (multiple windows open, multiple programs active, plus streaming, etc.). But, generally speaking, all of the reputable processors are going to have a low enough lag that it won't make much difference to an everyday user.

Basically, Celeron and Pentium processors are like cousins - they're both from Intel, but Pentiums pack a bit more punch than Celerons in terms of performance. As for AMD, they've got their own lineup that's pretty competitive too.
Picking the best processor for your needs really depends on what you'll be using your computer for. If you're just doing light tasks like web browsing and word processing, a Celeron might do the trick. But if you're into gaming or video editing, you might wanna spring for a Pentium or AMD processor for better performance.
Oh, and if you're still figuring things out, I stumbled upon one option where you can find a computer CPU for sale at https://starla.uk/product-category/pc-components/processors-cpu/ . Might be worth a look if you're ready to dive into the world of PC building.

The manufacturer and the Model ID #s used. A+ will want you to know the different models for repair purposes. To me I have used all of them with little difference besides the sockets used on the main board.

Always buy the most RAM you can get. Never found processors to be a big deal for normal work, unless you are a gamer or do heavy graphics work.

First of all, a celeron processor is old school, as is a Pentium processor... Regardless of what you will be doing, use the best new processor you can afford, and make sure you get a computer, laptop or desktop with a minimum of 16GB of RAM... 8 GB is not enough with a 64-bit processor, which is standard these days... Also, if you can afford it, go with a solid-state hard drive as these process data so much faster... If you can't afford that, get a computer with a 7200 RPM hard drive with some thing larger than 512 GB... 1 GB is pretty much standard... As for brands, stick with HP, Dell, Acer, or other name brands for reliability reasons... Let me know what you have in mind & I will let you know if it is a good deal or not... I work in IT and know what's good & what isn't...

what is your budget, what is the Computer primarily for. and just how mush usage per day?
If its just simple book keeping, internet browsing, and light Office work, then an I7 or better CPU would be fine, just make sure 16g of RAM, and at least 1 TB of storage, you would prefer SSD drive over an HDD, but if its just for light work and browsing, the HDD would do fine and cost less.

If its for Gaming then you want something similar to these specs:

Standing screen display size 17.3 Inches
Screen Resolution 3840x2160
Processor 2.4 GHz Intel_Mobile_CPU
RAM 64 GB DDR4
Hard Drive 2 TB SSD
Graphics Coprocessor RTX™ 3080 (Features Max-Q Technologies)
Chipset Brand NVIDIA
Card Description Dedicated
Graphics Card Ram Size 8.00
Other Technical Details
Brand HIDevolution
Series AERO 17 HDR YC-9US4760SP
Item model number A17-YC-9US4760SP-HID2
Hardware Platform PC
Operating System Windows 10 Pro
Item Weight 5.5 pounds
Product Dimensions 15.6 x 10.6 x 0.84 inches
Item Dimensions LxWxH 15.6 x 10.6 x 0.84 inches
Color I9-10980HK | RTX 3080
Processor Brand Intel
Processor Count 8
Computer Memory Type SODIMM
Hard Drive Interface Solid State

Mind you, this gaming laptop costs roughly $4k.