Fift and TVM assembly
Fift is stack-based programming language that has TON-specific features and therefore can work with cells. TVM assembly is also a stack-based programming language, also specific to TON, and it also can work with cells. So what's the difference between them?
The difference
Fift is executed at compile-time - when your compiler builds smart-contract code BOC, after FunC code is processed. Fift can look differently:
// tuple primitives
x{6F0} @Defop(4u) TUPLE
x{6F00} @Defop NIL
x{6F01} @Defop SINGLE
x{6F02} dup @Defop PAIR @Defop CONS
TVM opcode definitions in Asm.fif
"Asm.fif" include
<{ SETCP0 DUP IFNOTRET // return if recv_internal
   DUP 85143 INT EQUAL OVER 78748 INT EQUAL OR IFJMP:<{ // "seqno" and "get_public_key" get-methods
     1 INT AND c4 PUSHCTR CTOS 32 LDU 32 LDU NIP 256 PLDU CONDSEL  // cnt or pubk
   }>
   INC 32 THROWIF	// fail unless recv_external
   9 PUSHPOW2 LDSLICEX DUP 32 LDU 32 LDU 32 LDU 	//  signature in_msg subwallet_id valid_until msg_seqno cs
   NOW s1 s3 XCHG LEQ 35 THROWIF	//  signature in_msg subwallet_id cs msg_seqno
   c4 PUSH CTOS 32 LDU 32 LDU 256 LDU ENDS	//  signature in_msg subwallet_id cs msg_seqno stored_seqno stored_subwallet public_key
   s3 s2 XCPU EQUAL 33 THROWIFNOT	//  signature in_msg subwallet_id cs public_key stored_seqno stored_subwallet
   s4 s4 XCPU EQUAL 34 THROWIFNOT	//  signature in_msg stored_subwallet cs public_key stored_seqno
   s0 s4 XCHG HASHSU	//  signature stored_seqno stored_subwallet cs public_key msg_hash
   s0 s5 s5 XC2PU	//  public_key stored_seqno stored_subwallet cs msg_hash signature public_key
   CHKSIGNU 35 THROWIFNOT	//  public_key stored_seqno stored_subwallet cs
   ACCEPT
   WHILE:<{
     DUP SREFS	//  public_key stored_seqno stored_subwallet cs _51
   }>DO<{	//  public_key stored_seqno stored_subwallet cs
     8 LDU LDREF s0 s2 XCHG	//  public_key stored_seqno stored_subwallet cs _56 mode
     SENDRAWMSG
   }>	//  public_key stored_seqno stored_subwallet cs
   ENDS SWAP INC	//  public_key stored_subwallet seqno'
   NEWC 32 STU 32 STU 256 STU ENDC c4 POP
}>c