I'm hoping someone can clairify this as I have learnt two different methods from Train signal Chris Bryant and CBT Nuggets. and I dont know which one is correct.

I have watched each video 3 times each, but have changed the IP addresses and host names because obviously they use different ones.
Chris Bryant states in his videos that if a Host A (10.1.1.2)wants to send a packet onto Host B (192.168.0.5) which is on a different network, it will send out an arp broadcast saying "what is the MAC address of Host B on IP address 192.168.0.5). The default gateway that Host A is connected to replies back by proxy (called proxy arp). It basically pretends to be the MAC address for Host B but Host A doesn't know this fact. Host A now has its defaults gateway's MAC address and has associated it with the destination IP of 192.168.0.5. The entries are added to the host A's arp cache. Frame is sent onto the default gateway.
Jeremy from CBT nuggets describes it differently. He states that Host A would send out an ARP for its default gateway after it discovers from looking at the subnet mask that Host B isn't on his LAN and Host A's routing table tells him where to send it.Host A's default gateway replies back to the ARP request with his MAC address and now Host A adds this information to the frame as "destination MAC" but the destination IP will belong to Host B (192.168.0.5)
I appreciate both methods probably have the same desired effect..i.e. the sending computer gets the MAC address of the local router, but is it done by proxy arp (Bryant) or is it Jeremy's method which suggests to me that host A is pretty smart and knows whats going on(can't think of another way to put it)
perhaps it doesn't matter too much? i dont know personally, but on another topic, i have also noticed that Jeremy from CBT states that its the sender host that determines the size of TCP windowing (flow control) whereas Chris Bryant states explicitly that it is the receiver host that tells the sender how many packets he can send. Bit of a contradiction.
thanks