Definition of 'Markup'
The difference between an investment's lowest current offering price among dealers and the higher price a dealer charges a customer. Markups occur when dealers act as principals (buying and selling securities from their own accounts, at their own risk), as opposed to brokers (receiving a fee for facilitating a transaction). 
 Investopedia explains 'Markup'
Certain securities are available for purchase by retail investors from dealers who sell the securities directly from their own accounts. The dealer's only compensation for the sale comes in the form of the markup, the difference between the price the security was purchased at and the price the dealer charges to the retail investor. The dealer assumes some risk by acting in this capacity, as the market price of the security in his or her inventory could drop before he/she is able to sell to investors.

Note that most dealers are also brokers, and vice versa, so the term broker-dealer is common.
 
Definition of 'Markdown'
The difference between the highest current bid price among broker-dealers in the market and the lower price that a dealer charges a customer. 
 Investopedia explains 'Markdown'
The broker offers a lower price to try stimulate trading in hopes that they will make the money back on the extra commissions.