1. 1H p 2D p 3C
This bid is game forcing. Opener is promising 15+ or equivalent
2... 1H p 1Nt 2D 3 C
I play this bid as game forcing also...but here because responder limited their hand it shows an even bigger hand...about the same as a jump shift or equivalent in playing strength...
3. 1H p 1Nt 2D P
Openers pass may show a couple of things
1. Minimum opener
2. A good opener with diamonds (willingness to penalise)
3. No other convenient bid
4. 1H p 2D p 2Nt
In sayc this shows a minimum usually balanced opener with 12-14..
The answers for 1 and 4 are different in 2/1...In 1 you are already in a game forcing auction so depending on style 3c may show pattern and not necessarily promise extra points. In 2 2nt can be 12-14 and 18+.
In the hand shown presuming spades and hearts transposed or it was opened 1s then the rebid is 2nt in both sayc and 2/1 - minimum balanced.