Sometimes the words ‘keyboard’ and ‘synthesizer’ are used interchangeably. It could be argued that a synthesizer is in fact a keyboard, using the broader definition of the word. That would make pianos, electric pianos, organs and harpsichords all keyboard instruments. Most of the time though, referring to a keyboard is referring to a specific musical instrument.
Probably what most of us identify as keyboards are very portable, electronic musical instruments that seem to be only about half the length of a piano (they typically have 4 or 5 octaves) and they require only a light touch to press the keys. Keyboards can be very cheap compared to other musical instruments and they are certainly cheaper than pianos and electric pianos.
As well as having the keyboard part, they have built in different rhythms that you can use to accompany yourself, they also have a selection of instruments that you can have your music sound like and a lot of them have pre-programed tunes that you can just push a button to listen to. Some keyboards can be quite cheap and nasty and these ones are more like toys for kids to muck around on rather than being a real musical instrument.
The keyboards that are definitely not toys are okay for being a substitute for a piano, when a person first takes piano lessons. I have had a number of piano students start this way and while it is not ideal, it is definitely adequate for maybe a year or two. Anything beyond this time frame can result in the piano student getting quite frustrated at the limitations of a keyboard.
The most significant difference between a keyboard and a synthesizer is that with the synthesizer you can get very creative by digitally sampling various sounds and then being able to electronically manipulate these sounds.
Synthesizers are more suited to people that are into electronic music and creating their own electronic music. For this group of people, a keyboard would not be sufficient to be able to do what they wish to do.
As I have just stated, synthesizers are more suited to people that are into electronic music and creating different sounds. Unless you are one of these people, then I would not recommend a synthesizer as a first instrument, I think it would make more sense to start with a piano or keyboard. Using a synthesizer later down the track, especially combined with a traditional piano could be a wonderful creative outlet and a way of expanding your skills.
On a practical level, it is important to note that keyboards have built in speakers – it is ready to go straight out of the box. A synthesizer does not have built in speakers. It needs to be plugged into an amplifier or conversely have headphones plugged in, in order to hear the sound.
Synthesizers tend to be used by professional musicians or experienced amateurs who have a big interest in electronic music, whereas keyboards tend to be an entry level instrument, which can be used as a cheaper option instead of a piano.