Usually when I take the test, I get some form of ISTP with strong I and T and moderate S and P. Sometimes I get INTJ or ISTJ, but never have I gotten INTP.

I've taken the test from the first link before and I usually get INTJ.
Today I got
ISTJ
Introvert(67%) Sensing(1%) Thinking(88%) Judging(44%)
You have distinct preference of Introversion over Extraversion (67%)
You have marginal or no preference of Sensing over Intuition (1%)
You have strong preference of Thinking over Feeling (88%)
You have moderate preference of Judging over Perceiving (44%)

I've never taken the second one before. I'm not sure I like it. I feel so in-the-middle on certain things with no usual lean toward one or the other.
ISTJ
Introverted (I) 83.33% Extroverted (E) 16.67%
Sensing (S) 62.5% Intuitive (N) 37.5%
Thinking (T) 70.83% Feeling (F) 29.17%
Judging (J) 54.17% Perceiving (P) 45.83%
ISTJ - "Trustee". Decisiveness in practical affairs. Guardian of time- honored institutions. Dependable. 11.6% of total population.

I was definitely IST on the last one, and I was torn between J and P. I like schedules and given nothing to do I will do nothing. But I've also heard that procrastinators usually fall heavily under P, and I am notorious for procrastination. I will put off making decisions as long as I can while some facts are unclear or unknown, but once I make it it drives me nuts to stray from it.

Reading up on the personality types on the link in the OP is very interesting. ISTJ does seem to describe my generally "cold, robotic nature" and my tendency towards honesty and confessions, my general inability to express my feelings, insensitivity, etc etc. Actually it sounds more accurate to me than the ISTP type ever did, although there are issues that I take from each side. I've always been very unsure of my J/P typing.