Not always. I was going to restore a Faema E61 and discovered that the basic model is almost identical to the original. Parts are interchangeable. It’s manual, it’s beautiful and it’s expensive.
I went down the espresso rabbit hole during covid, as did a good buddy of mine. We both upgraded from setups in the ~$1k range and are experiencing much better results in the cup. Obviously you'll see diminishing returns at some price point, but most of my friends/family agree that a latte from my new setup is noticeably better than one from my old setup.
My grinder is a Weber EG-1. It has really large (80mm) flat burrs. Very forgiving; like I don't have to be dialed in perfectly for the espresso to be very good. It's essentially a cafe quality grinder, but optimized for a single-dose flow.
My machine is an Olympia Cremina, which is a manual lever machine. I've modified it with a pressure profiler to control and track the pressure of the shot I'm pulling. All that manual control is really nice for the kind of coffees I like which are usually naturally-processed light roasts. However, manual levers are not for everyone and have a definite learning curve.
If you're curious about either of those, James Hoffmann has good reviews of them both on YT.
I really enjoy the nerdiness and tactile feedback of the manual lever, but if I didn't want go manual, I'd look at a Decent DE-1.
If I had to shave a bit off that budget, I think I'd go with a Rancilio Silvia Pro X, which is half the cost.
I'm not sure if OP bought an all-in-one, but I wouldn't recommend those, they don't do any of their tasks particularly well, when you could spend the same amount and get much better coffee.
You'd be correct. Check out some recommendations on /r/coffee for a grinder, and also James Hoffman's on YouTube.