I have a basic TCP client and TCP server in C++.   The TCP client
connects to the server, and after a setup phase starts to transmit a
file to the TCP server using multiple packets (fixed amount of bytes,
except for the last packet). This is accomplished by using a for loop
and the "int send(socket, buffer, bufferlength, 0)" function.

When I read the packets using  "int recv(socket, buffer, 1500, 0)" the
number returned by the function is 1500, although the "data" packets
that I have sent each contains less bytes (1310 bytes).  It seems that
with each recv() function, I get 1500 bytes from the network buffer,
and that I have lost "synchronisation" - I don't read packet for
packet, but a chunk of the network buffer. Is this the normal
operation of TCP, or did I break something along the way?  (I would
hope that each recv function would return 1310, the size of the
original packet.)

But I tell you:
TCP is stream based. There are now record borders (you'd use UDP
for that). You have to transmit the record size in your packet
structure.