They're similar by both being primarily in-memory, but that's about it.
Redis is an in-memory key-value database. It can persist data to disk if configure it, but it keeps the entire dataset in memory so you need enough RAM for that. The key-value architecture allows various different data types so you can store a value as a simple string or lists, sets, hashes, etc. Basically all the data structures you can use inside of a programming language are available in Redis natively.
SQL Server Hekaton (In-Memory OLTP) is a new engine designed to run relational tables in memory. All the data for these tables is kept in RAM but also stored to disk so they are fully durable.
Hekaton can take individual tables in a SQL Server database and run them in a different process using MVCC (instead of pages and locks) and other optimizations so operations are thousands of times faster than the traditional disk-based engine. There is a lot of research that went into this and the primary use-case would be to take a table that is under heavy load and switch it to run in-memory to increase performance and scalability.
Hekaton was not meant to run an entire database in memory (although you can do that if you really want to) but rather as a new engine designed to handle specific cases while keeping the interface the same. Everything to the end-user is identical to the rest of SQL Server: you can use SQL, stored procedures, triggers, indexes, atomic operations with ACID properties and you can work seamlessly with data in both regular and in-memory tables.
Because of the performance potential of Hekaton, you can use it to replace Redis if you need the speed and want to model your data within traditional relational tables. If you need the other key-value and data structure features of Redis, you're better off staying with that.
With SQL 2016 SP1 and newer, all tiers of SQL Server now have access to the same features and the only difference is pricing for support and capacity.