Determine the architecture of a Mac from the command line or script?

There are many ways, but try uname -a.

uname -m seems to output the same information as /bin/arch.

arch is available in /usr/bin/arch

You can get OS version information with sw_vers

$ sw_vers
ProductName:    Mac OS X
ProductVersion: 10.6.3
BuildVersion:   10D573
$ sw_vers -productVersion
10.6.3

You can use sysctl to get information about your CPU:

$ sysctl machdep.cpu.brand_string
machdep.cpu.brand_string: Apple M1 Pro

Now you can take this string and search in the internet to get details about this CPU brand.

If you want more information about the CPU you can use this command:

$ sysctl machdep.cpu
machdep.cpu.cores_per_package: 10
machdep.cpu.core_count: 10
machdep.cpu.logical_per_package: 10
machdep.cpu.thread_count: 10
machdep.cpu.brand_string: Apple M1 Pro
machdep.cpu.features: FPU VME DE PSE TSC MSR PAE MCE CX8 APIC SEP MTRR PGE MCA CMOV PAT PSE36 CLFSH DS ACPI MMX FXSR SSE SSE2 SS HTT TM PBE SSE3 PCLMULQDQ DTSE64 MON DSCPL VMX EST TM2 SSSE3 CX16 TPR PDCM SSE4.1 SSE4.2 AES SEGLIM64
machdep.cpu.feature_bits: 151121000215084031
machdep.cpu.family: 6