Ooh, what a question to start! This one could be an essay...

MPs sit in the UK Parliament, in the House of Commons. There are 650 of them, and each represents a constituency of roughly equal size somewhere in the UK. They are elected at general elections, at least every 5 years. They earn a salary of about £80k, and work full time, splitting their time between work in Parliament and in their constituency. They vote to make laws, and some will be chosen to become ministers, who run the government and propose most laws.
Local councillors belong to county, district and unitary authority councils. There are many thousands of them, and they represent wards that are much smaller than an MP's constituency. Each ward tends to have between one and three councillors representing it, depending on the council. Councillors are elected every 4 years in England and every 5 years in Wales and Scotland, though in England they aren't all elected on the same schedule, so there are local elections somewhere every year. Councillors tend not to be paid a full-time salary, and will work another job at least part-time. However again, some councillors on each council are chosen to become part of the cabinet as portfolio holders, and this usually brings a proper salary, albeit a much smaller one than a minister. Councillors are not able to make laws, but the laws in place give them some 'executive' powers to make some decisions on things like planning rules, education, social care and public services like libraries.