No they are not, but they can sound close depending on the settings of both pedals.

Let me talk you through how they are:

The TS 808 is good for creating mild overdrive to your amp, even when the pedal itself is not being pushed into overdrive.
The TS 808 is not able to give you a clean boost, no matter what you do. Maybe modded versions are, but I am talking about the stock, reissue version from 2004. No clean boost.

The OD-1 can give you a clean boost, the pedal does not have that much volume, but it will be able to get your amp to sound louder even when the overdrive control is all the way down.
The OD-1 does have a slight mid range sound, characteristic of Marshall amps. You will not be able to get rid of this sound, no matter how you set the controls. All it all, use the OD-1 and your amp starts to sound like a Marshall.

The TS 808 does have more volume compared to the OD-1, it also has more bass compared to the OD-1, which may surprise some people. The mid-range boost, a lot of people mention about the TS 808, is of a very different nature as that compared the the OD-1: OD-1’s mid range is really the Marshall sound, TS 808’s midrange is neutral, hence the pedal being so good to give that smooth push towards your amp. (It works best with Valve amps, not so great with Transistor amps!)

The overdrive of the TS 808 is smoother compared to the OD-1, it is also neutral, the OD-1’s overdrive is Marshall: Keep overdrive down and the sound is mild, open up the overdrive and the OD-1 will give you a very thick sound.

You are able to get both pedals to sound somewhat the same depending on the settings of the controls, but remember, they can also sound very different.

There are some videos on You Tube where people compare both pedals, some of those do not really show the differences between both pedals. It really depends on what the creater of the video has in mind and what he/she feels is important to show in the video.

Stay tuned for more pedal talk for next few articles.
Eddie