MACA is broader term that covers any sort of wireless media access control. It encompasses CSMA/CA as well as a number of other protocols.
CSMA/CD and CSMA/CA are very similar. The primary difference between CSMA/CD and CSMA/CA is that CSMA/CD requires that a host be able to both transmit and receive on the medium at the same time.
CSMA/CD was originally used in 802.3 communication because all hosts could see traffic from all other hosts, however most modern 802.3 communication is full duplex and as such does not use CSMA/CD.
CSMA/CA is used in 802.11 communication because physics makes it very difficult or impossible for a device to both transmit and receive at the same time on the same frequency (even if you use a separate transmitter and receiver to attempt this, the proximity of the transmitter to the receiver will tend to "drown out" any other signal).
Neither CSMA/CD nor CSMA/CA make use of RTS/CTS as part of their protocol, they are three entirely separate protocols. However you can use RTS/CTS with either one, although it only really makes sense with CSMA/CA in certain circumstances.
RTS/CTS (or CTS-to-self) is an option in 802.11 for a few reasons. Primarily it is part of a protection mechanism to allow older 802.11 devices and newer 802.11 devices to communicate properly (specifically 802.11b or earlier devices with 802.11g or later devices - many DSSS devices wouldn't recognize OFDM traffic as another 802.11 device). It can also be used to resolve a number of different issues. However due to it's significant impact on 802.11 performance, it is not recommend to use if you can avoid it. CSMA/CA is always used for 802.11 traffic whether you use RTS/CTS or not.
Edit: As requested in the comment, however this will make the answer significantly longer, even keeping the explanation on the simplistic side.
RTS/CTS was originally implemented in old serial devices that used half-duplex communication to determine when data could be sent. When full-duplex serial communication was implemented, RTS/CTS was repurposed to allow serial communications to implement flow control. This RTS/CTS worked by sending a signal over separate conductors than those used to actually transmit the data.
Since 802.11 doesn't have different connectors, it's RTS/CTS is different in that one side sends a RTS frame and waits for a CTS response (which will include an amount of time being reserved). Other stations that hear the CTS are supposed to back off for that period of time to leave the air clear. The major drawback is that RTS/CTS frames, similar to other management frames, must be heard by all stations and are transmitted at the lowest common base data rate; this it typically significantly lower that the maximum data rate (i.e. often this is 1 Mbps when the max data rate today is often 300+ Mbps). This means that each RTS/CTS frame transmitted in the air can take as much time as 300+ data frames.
To reduce this performance impact, 802.11 devices can implement a CTS-to-self mechanism instead, reserving the air for themselves. However this should only be done when used for the purposes of providing legacy support (many 802.11b devices do not recognize 802.11g signalling as 802.11 traffic and this helps prevent them from creating collisions). If you are trying to alleviate hidden node problems (i.e. two or more stations that are able to associate to the same access point, but can't see each other and end up tranmitting at the same time), you need to use full RTS/CTS as you need the CTS to originate from the AP. In addition, both mechanisms (RTS/CTS and CTS-to-self) can introduce performance issues to any neighboring BSS that is exposed to the CTS frames as they will be required to back off as well.
CSMA/CD starts by a device listening to the medium to see if it is clear of other transmissions. If the medium is clear, it will start transmitting and if the medium isn't clear it will back off for a random amount of time and then listen again.
When the device is transmitting, if it receives a signal at the same time, it will trigger the CD part of the process. To resolve the collision, the device immediately stops sending it's data but continues to transmit a "jam signal" to allow all devices to detect the collision and back off for a random amount of time. The device that was transmitting when the collision occurred will also increment a retransmission counter and try the frame again unless it has reached it's maximum retries.
CSMA/CA starts the same as CSMA/CD; a device listens to the medium to see if it is clear. If it is then it will begin transmitting otherwise it will back off a random time and try again. However, as I mentioned earlier, it is not possible for a wireless device to transmit and receive at the same time, so it cannot detect a collision. Then how does a device know if it experienced a collision? It can't and doesn't, hence why it isn't CSMA/CD.
In CSMA/CA the receiving station will send an ACK for received data frames, if the sending station doesn't receive an ACK, it assumes the frame is lost (due to collision, interference, noise, or any other reason) and retransmit. In 802.11 there are often two retransmission counters, one that will cause the next retransmission to use a lower data rate (i.e. higher data rates require better signal quality, so perhaps a frame the fails to transmit at a higher data rate will succeed at a lower data rate) and one for the maximum number of retransmissions.
Well, that is a brief explanation of how they work. Hopefully this is enough to help you understand them a bit more.
Best Answer
A probability of 0 doesn't make sense unless you don't want to transfer ever. You need to choose something between 0 and 1.
The algorithm waiting for the start of the slot time reduces the chance that someone else has just started transmitting but the carrier hasn't reached you yet. Overall, it increases the effiency of CSMA by reducing the penalty of a collision.
Not using the first possible slot but working with a probability is way to get a fairer distribution of traffic. It greatly reduces the possibility for a busy sender to hog the medium.
The
1-pprobability for the skipping the first slot just expresses that you either send now (probability p) or on the very next slot (probability 1-p). You don't throw the dice for each slot again and again.