I saw that term used in my book "Captured Tanks Under The German Flag" featuring Russian tanks. What is meant by that term? Looking it up ha brought no answers.

this might be one answer:
http://www.network54.com/Forum/47207/thread/1026373076/last-1026643016/View+Thread
somesupport for this theory can be found here:
https://books.google.se/books?id=xKGwCwAAQBAJ&pg=PA38&lpg=PA38&dq=%22pursuit+tanks%22&source=bl&ots=Nl_luWiWEs&sig=Q1eFNrhJy94auGxotwJOMpAUZUQ&hl=en&sa=X&ved=0ahUKEwj76qrsjL_XAhVPK1AKHZc0DFsQ6AEIWDAO#v=onepage&q=%22pursuit%20tanks%22&f=false


this could be another answer:
https://books.google.se/books?id=WBeeBAAAQBAJ&pg=PT21&lpg=PT21&dq=%22pursuit+tanks%22&source=bl&ots=2jKB-oa57K&sig=e1ZFhBMM2SLZ9-hugZ5b9_stwjE&hl=en&sa=X&ved=0ahUKEwj76qrsjL_XAhVPK1AKHZc0DFsQ6AEITTAL#v=onepage&q=%22pursuit%20tanks%22&f=false
From the days when the tactical thinking was that there were two types of tanks, infantry tanks and cavalry tanks.

/ Robin

The Germans captured many enemy tanks from all sides and impressed them into their Panzerwaffe. They are known as "Beutepanzers". When the Wehrmacht invaded the Soviet Union they captured many T-34's, Kv-1's and others and used them. Some they remanufactured to make them more compatible with German service.

I have that book, it's very interesting. Although T 34 (r) Beutepanzers did fight on the frontline - notably with Das Reich and GD, many captured tanks were used as mopping up vehicles, as they were sometimes fired upon by friendly forces due to their unique silhouttes. The term "pursuit tank" would be a way to describe these operations. As you probably know, many tanks, especially light or obsolete ones, were destined for second-line units, anti-partisan operations and airfield and garrison patrols. Many were also converted to tractors, SPGs, etc. Some were used as pillboxes or target practice.

Pictures of captured equipment used by Germany
http://www.achtungpanzer.com/ctpic.htm

Captured T-34 pulled from marsh, note the balkenkreuz on the hull.
https://m.youtube.com/watch?v=YNJ-acc9Qsk