If you played both for longer than the intro, you would notice that there are difference in movement, weapon-handling, AI-behaviour, puzzles, and pretty much everything.
For example, you basically can't jump in Black Mesa. What they call "jump", I call "standing on your toes". In Half-Life, I can jump over a handrail no problem and on some crates. Black Mesa? I can't do anything involving jumping unless I constantly crouch-jump. Which makes crouch-jumps as seperate feature complete pointless when it's THE ONLY THING I am allowed to use.
Other example would be the MP5 (or M4 in Half-Life with HD pack).
HL - 50 rounds, 250 spare, full-auto with semi-auto on tapping, good on mid-range and okay on long range.
BMS - 30 rounds, 120 spare, full-auto with BURST-FIRE on tapping, short range only.
Shotgun - a secret one in "Office complex" early, with two near the end in HL, somewhere in the middle of "We've Got Hostile" in BMS.
Crowbar - HL gives you pretty much right away, you only need to deal with one headcrab. BMS? Well, have fun dodging like 50 zombies for half an hour because your only way of defense is a guard unable to shoot. And once you got the crowbar, the first thing you're supposed to smash most likely KILLS YOU ON THE SPOT DUE A EXPLOSIVE CRATE AMONG THE THINGS YOU HAVE TO BREAK TO CONTINUE IN THE FIRST PLACE!
Yeah, the two games are like night and day when it comes to gameplay. With Black Mesa doing everything wrong I can think of.