buying it, you pay no monthly, Products and you get free updates, but no upgrades (for free) when adobe releases the next version.
with monthly subscription (photographer's lr and ps for $10/mo is most economical) you get free updates AND free (as long as you maintain your subscription) upgrades, Creative Cloud pricing and membership plans | Adobe Creative Cloud
If you'll by software then you'll own copy of that software. If you'll pay monthly then you'll pay for renting it no matter if you using it or not. Read this forum about more surprises you can find with monthly fees.