These are two chips from two different NXP chip families - MIFARE® and NTAG®. The MIFARE range is targeted towards event ticketing, transport ticketing and vouchers. The NTAG range is more mobile focused with an emphasis on marketing, identification and authentication.
The MIFARE Ultralight EV1 is an updated version of the Ultralight which was originally launched in 2003. It's a widely used chip with limited features but strong scan performance. There are two variants with different memory capacities - a 48 byte user memory version and 128 byte user memory version. The smaller memory version is more common and if you are buying a tag or product, it's likely that this will be specified by default.
The NTAG213 is part of the NTAG21x series of chips and along with the NTAG210, is the most common. It's a full featured tag with enough memory for almost all standard use cases. Widely available, it's found in a very broad range of tags and products.